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Graph Theory

Discrete Mathematics

Member of the Royal Danish Academy
of Sciences and Letters

Editor-in-Chief of the Journal of
Graph Theory.

Editor of Combinatorica, The Journal
of Combinatorial Theory, Ser B, Discrete Mathematics, European Journal
of Combinatorics, Electronic Journal of Combinatorics, Australiasial Journal of
Combinatorics

Born August 22, 1948 at Grindsted, Denmark.

**
Degrees**

Cand.Scient. Degree (Master's Degree) June 1972 from Aarhus University.

Ph.D. October 1976 from University of Waterloo.

**
Employment**

Teaching Assistant at the Institute of Mathematics, Aarhus University, August 1968 – July 1972.

Assistant Professor at Mathematics Institute, Aarhus, August 1972 – July 1976.

Associate Professor (lektor) at the Institute of Mathematics, Aarhus University, August 1976 - July 1981.

Professor of Mathematics at the Technical University of Denmark (DTU) since August 1981.

**
**

**
Visiting and adjunct positions**

Visiting Associate Professor at Louisiana State University, Spring 1980.

Visiting William Allen Neilson Research Professor at Smith College, Massachusetts, Fall 1987.

Distinguished Visiting Scholar at Western Michigan University, May 1988.

Professor with Term Chair at University of Pennsylvania, Fall 1988.

Adjunct Professor, University of Waterloo, 1994-2001.

William Evans Visiting Fellow, University of Otago, Dunedin New Zealand, February-March 2002.

Visiting Rothschild Professor at the Isaac Newton Institute and Cambridge University, May 2008 (http://www.newton.ac.uk/rothschild.html shows the impressive list of previous invitees, characterized as “pre-eminent mathematician around the World.” )

Distinguished Adjunct Professor under the Highly Cited Research Project, King Abdulaziz University 2011-

One-month visiting professorships at Université Paris-Sud, Université Claude Bernard Lyon (both France), Universität Bielefeld, Universität Chemnitz (both Germany) Universitá di Milano, Universitá di Torino (both Italy), University of Melbourne (Australia), University of Otago (New Zealand), and University of Malta.

**
Editorial positions**

Chief editor of the Journal of Graph Theory since 1989 (Associate editor 1979-89).

Editor of the Electronic of Journal of Combinatorics since 2002 (Chief editor 2002-2013).

Member of the editorial boards Discrete Mathematics (since 1979), Journal of Combinatorial Theory Ser. B (since 1982), Aequationes Mathematica (1984-1991), Combinatorica (since 1985), European Journal of Combinatorics (since 1988), SIAM Journal of Discrete Mathematics (1989-1993), The Australasian Journal of Combinatorics (since 2010).

**
Awards, Recognitions, Fellowships, and other professional characteristica**

Dedicatory Award of the 6th International Conference on the Theory and Applications of Graphs, Western Michigan University, May 1988.

Erdös number 1, 1989 ( Erdös number 2, 1973)

Member of the Royal Danish Academy of Sciences and Letters since 1990.

Invited lecture at the International Congress of Mathematicians, Kyoto 1990.

Founding Fellow and Member of Council of the Institute of Combinatorics and its Applications (Winnipeg, Canada) since 1990.

Lester R. Ford Award (Mathematical Association of America) 1993.

Organizer of Tagung über Graphenteorie, Forschungsinstitut Oberwolfach, 26.6-2.7 l994.

Knight of Dannebrog 1995

Member of the Conseil Scientifique Université Claude Bernard Lyon 1999- 2003.

Member of The Canada Research Chairs College of Reviewers 2001-2005.

Member of the Ostrowski Prize Committee 2001- 2005.

Faculty of Mathematics Alumni Achievement Medal, University of Waterloo, 2005.

External Assessor at the University of Malaya 2008-2011.

Included (since 2003) on the ISI Web of Knowledge list (highlycited.com) of the most cited mathematicians Worldwide.

Danish Magisterforening Research Prize 2012.

**
Current Funding ID**

ERC Advanced Grant "GRACOL" (Graph Colorings and Decompositions) 2013-2018.

Principal Investigator of the FNU (Danish Research Council for Nature and Universe) grant ”AlgoDisc" 2013-2016 (DFF-1323-00178).

**Publications:**

1 On randomly Hamiltonian graphs, Math. Ann. 200 (1973) 195-208.

2 Antidirected Hamilton circuits and paths in tournaments, Math. Ann.
201 (1973) 231-238.

3 (with G.A Dirac) Graphs in which every finite path is contained in
a circuit, Math. Ann. 203 (1973) 65-75.

4 Graphs in which every path is contained in a Hamilton path, J. Reine
Angew. Math. 268/269 (1974) 271-282.

5 Some homeomorphism properties of graphs, Math. Nachr. 64 (1974) 119-133.

6 (with B.Å. Sørensen) On k-rails in graphs, J. Combinatorial
Theory B 17 (1974) 143-159.

7 A minimal condition implying a special K4-subdivision in a graph,
Arch. Math. 15 (1974) 210-215.

8 Hypohamiltonian and hypotraceable graphs, Discrete Math. 9 (1974)
91-96.

9 On hypohamiltonian graphs, Discrete Math. 10 (1974) 383-390.

10 (with G.A. Dirac) On the existence of certain subgraphs in infinite
graphs, Nederl. Akad. Vetensch. Indag. Math. 36 (1974) 406-410.

11 Transversals of circuits in the lexicographic product of directed
graphs, Math. Sci. Hum. 51 (1975) 43-45.

12 Homeomorphism properties of graphs, Teorie Combinatorie, Atti Dei
Convegni Lincei 17 (1976) 269-277.

13 (with R. Häggkvist) On pancyclic digraphs, J. Combinatorial
Theory B 20 (1976) 20-40.

14 (with F. Harary) Anticritical graphs, Math. Proc. Cam. Phil. Soc.
79 (1976) 11-18.

15 (with K.B. Reid) Edge sets contained in circuits, Israel J. Math.
24 (1976) 305-319.

16 (with K.B. Reid) Strongly selfcomplementary and hereditarily isomorphic
tournaments, Monatshefte für Math. 81 (1976) 291-304.

17 Planar and infinite hypohamiltonian and hypotraceable graphs, Discrete
Math. 14 (1976) 377-389.

18 Note on circuits containing specified edges, J. Combinatorial Theory
B 22 (1977) 279-280.

19 An Ore-type condition implying a digraph to be pancyclic, Discrete
Math. 19 (1977) 85-92.

20 (with J.A. Bondy) A short proof of Meyniel's Theorem, Discrete Math.
19 (1977) 195-197.

21 Counterexamples to the Edge Reconstruction Conjecture for infinite
graphs, Discrete Math. 19 (1977) 293-295.

22 Straight line representations of infinite planar graphs, J. London
Math. Soc. 16 (1977) 411-423.

23 (with V. Chvátal) Distance in orientations of graphs, J. Combinatorial
Theory B 24 (1978) 61-75.

24 On separating cycles in graphs, Discrete Math. 22 (1978) 57-73.

25 Hypohamiltonian graphs and digraphs, in:Proc. of the intern. conf.
on the Theory and Appl. of Graphs, Kalamazoo 1976, Springer Verlag (1978),
pp 557-571

26 Reconstructing 1-coherent locally finite trees, Comment. Mat. Helv.
53 (1978) 608-612.

27 Reconstructibility versus edge reconstructibility of infinite graphs,
Discrete Math. 24 (1978) 231-233.

28 Counterexamples to Faudree and Schelp's conjecture on Hamiltonian-connected
graphs, J. Graph Theory 2 (1978) 341-347

29 Hamiltonian paths in squares of infinite locally finite blocks, Annals
of Discrete Math. 3 (1979) 269-277.

30 Long cycles in digraphs with constraints on the degrees, in:Surveys
in Combinatorics, Proceedings of the Seventh British

Combinatorial Conference., London Math.
Soc. Lecture Note Ser. 38 (1979),pp 211-228.

31 (with V. Chvátal, H. Fleischner and J. Sheehan) Three-regular
subgraphs of four-regular graphs, J. Graph Theory 3 (1979) 371-386.

32 (with S.L. Hakimi and E.F. Schmeichel) On the number of Hamiltonian
cycles in a maximal planar graph, J. Graph Theory 3 (1979) 365-370.

33 (with L.D. Andersen) The cover-index of infinite graphs, Aequationes
Math. 20 (1980) 244-251.

34 Hamiltonian-connected tournaments, J. Combinational Theory B 28 (1980)
142-163.

35 On the number of Hamiltonian cycles in tournaments, Discrete Math.
31 (1980) 315-323.

36 (with M. Grötschel and Y. Wakabayashi) Hypotraceable digraphs,
J. Graph Theory 4 (1980) 377-381.

37 Planarity and duality of finite and infinite graphs, J. Combinatorial
Theory B 29 (1980) 244-271.

38 2-linked graphs, Europ. J. Combinatorics 1 (1980) 371-378.

39 Planarity and duality of graphs, in:Proc .11th. S-E Conf. on Combinatorics,
Graph Theory and Computing, Congr. Num. 28 (1980),pp 5-24.

40 Planar cubic hypohamiltonian and hypotraceable graphs, J. Combinatorial
Theory B 30 (1981) 36-44.

41 Long cycles in digraphs, Proc. London Math. Soc. 42 (1981) 231-251.

42 (with B. Toft) Non-separating induced cycles in graphs, J. Combinatorial
Theory B 31 (1981) 199-224.

43 Landau's Characterization of tournament score sequences, in: The
Theory and Applications of Graphs (eds. G. Chartrand et al.) John

Wiley and Sons (1981) pp. 589-591.

44 Non-separating cycles in k-connected graphs, J. Graph Theory 5 (1981)
351-354.

45 (with B. Bollobás) The size of connected hypergraphs with
prescribed covering number, J. Combinatorial Theory B 31 (1981) 150-155.

46 (with J.-C. Bermond) Cycles in digraphs - a survey, J. Graph Theory
5 (1981) 1-43.

47 A remark on factor theorems of Lovász and Tutte, J. Graph
Theory 5 (1981) 441-442.

48 Kuratowski's Theorem, J. Graph Theory 5 (1981) 225-241.

49 (with R. Häggkvist) Circuits through specified edges, Discrete
Math. 41 (1982) 29-34.

50 (with D.A. Holton, B.D. McKay and M.D. Plummer) A nine point theorem
for 3-connected cubic graphs, Combinatorica 2 (1982) 53-62.

51 Duality of infinite graphs, J. Combinatorial Theory B 33 (1982) 137-160.

52 (with M.C. Heydemann and D. Sotteau) Orientations of Hamiltonian
cycles in digraphs, Ars Combinatoria 14 (1982) 3-8.

53 Edge-disjoint Hamiltonian paths and cycles in tournaments, Proc.
London Math. Soc. 45 (1982) 151-168.

54 Infinite graphs, in: Further Selected Topics in Graph Theory (L.W.
Beineke and R.J. Wilson, eds.) Academic Press, London 1983,

pp, 129-160.

55 A theorem on paths in planar graphs, J. Graph Theory 7 (1983) 169-176.

56 Graph decomposition with constraints on the connectivity and minimum
degree, J. Graph Theory 7 (1983) 165-169.

57 Graph decomposition with applications to subdivisions and path systems
modulo k, J. Graph Theory 7 (1983) 261-271.

58 Cycles in graphs of uncountable chromatic number, Combinatorica 3
(1983) 133-134.

59 Deformations of plane graphs, J. Combinatorial Theory B 34
(1983) 244-257.

60 Disjoint cycles in digraphs, Combinatorica 3 (1983) 393-396.

61 Girth in graphs, J. Combinatorial Theory B 35 (1983) 129-141.

62 Subdivisions of graphs with large minimum degree, J. Graph Theory
8 (1984) 23-28.

63 Connectivity in tournaments in: Graph Theory and Combinatorics, A
volume in honour of Paul Erdös (B. Bollobás, ed.), Academic

Press, London 1984,pp. 305-313.

64 Plane representations of graphs, in: Progress in Graph Theory (J.A.
Bondy and U.S.R. Murty eds.) Academic Press, Toronto 1984,

pp. 43-69.

65 Grafteori - en introduktion (in Danish) Normat 32 (1984) 111-124.

66 A refinement of Kuratowski's theorem, J. Combinatorial Theory B 37
(1984) 245-253.

67 Even cycles in digraphs, Europ. J. Combinatorics 6 (1985) 85-89.

68 The 2-linkage problem for acyclic digraphs, Discrete Math. 55 (1985)
73-87.

69 Hamilton circuits in regular tournaments, Ann. Discrete Math. 27
(1985) 159-162.

70 (with R.E.L. Aldred and D.A. Holton) Cycles through four edges in
3-connected cubic graphs, Graphs and Combinatorics 1 (1985) 7-11.

71 Retracting-free double tracing of graphs, Ars Combinatoria 19 (1985)
63-68.

72 Gabriel Andrew Dirac, J. Graph Theory 9 (1985) 303-318.

73 Decomposition of graphs into chains, Bull. London Math. Soc. 18 (1986)
248-254.

74 Sign-nonsingular matrices and even cycles in directed graphs, Linear
Algebra Appl. 75 (1986) 27-41.

75 Interval representations of planar graphs, J. Combinatorial Theory
B 40 (1986) 9-20.

76 Reflections on graph theory, J. Graph Theory 10 (1986) 309-324.

77 (with G. Hahn) Path and cycle sub-Ramsey numbers and an edge colouring
conjecture, Discrete Math. 62 (1986) 29-33.

78 (with P. Seymour) Characterization of even digraphs, J. Combinatorial
Theory B42 (1987) 36-45.

79 Counterexamples to Adám's conjecture on arc reversals in directed
graphs, J. Combinatorial Theory B42 (1987) 128-130.

80 A characterization of locally finite vertex-transitive graphs, J.
Combinatorial Theory B 43 (1987) 116-119.

81 (with N. Alon, J. Kahn, D. Kleitman, M. Saks,and P. Seymour) Subgraphs
of large connectivity and chromatic number in graphs of

large chromatic number, J. Graph Theory
3 (1987) 367-371.

82 On digraphs with no two disjoint directed cycles, Combinatorica 7
(1987) 145-150.

83 (with P. Fraisse) Hamiltonian dicycles avoiding prescribed arcs in
tournaments, Graphs and Combinatorics 3 (1987) 239-250.

84 Paths, circuits and subdivisions, in: Selected Topics in Graph Theory
III (L.W. Beineke and R.J. Wilson, eds.), Academic Press

1988, pp. 97-131.

85 On the presence of disjoint subgraphs of a specified type, J. Graph
Theory 12 (1988) 101-111.

86 Arc reversals in tournaments, Discrete Math. 71 (1988) 73-86.

87 Rectilinear drawings of graphs, J. Graph Theory 12 (1988) 335-341.

88 Whitney's 2-switching theorem, cycle spaces, and arc mappings of
directed graph, J. Combinatorial Theory B 46 (1989) 257-291.

89 Configurations in graphs of large minimum degree, connectivity, or
chromatic number, Proc. 3rd. Internat. Conf. on Combinatorial

Mathematics, New York 1985, Ann. New York Acad.
Sci. 555 (1989) 402-412.

90 (with M. Watkins) Infinite vertex-transitive edge-transitive non-1-transitive
graphs, Proc. Amer. Math. Soc. 105 (1989) 258-261.

91 (with R. Aharoni) Infinite highly connected digraphs with no two
arc-disjoint spanning trees, J. Graph. Theory 13 (1989) 71-74.

92 The graph genus problem is NP-complete, J. Algorithms 10 (1989) 568-576.

93 When the sign-pattern of a matrix determines uniquely the sign pattern
of its inverse, Linear Algebra Appl. 119 (1989) 27-34.

94 (with P. Erdös, Y. Alavi, P.J. Malde, and A.J. Schwenk) Tight
bounds on the Chromatic sum of a connected graph, J. Graph Theory 13 (1989)
353-357.

95 Planar acyclic oriented graphs, Order 5 (1989) 349-361.

96 The converse of the Jordan curve theorem and characterization of
planar maps, Geometriae Dedicata 32 (1989) 53-57.

97 (with H. Wilf) On uniformly filled determinants, The College Mathematics
Journal 21 (1990) 135-137.

98 Resistances and currents in infinite electrical networks, J. Combinatorial
Theory B 49 (1990) 87-102.

99 Bidirectional retracting-free double tracings and upper embeddability
of graphs, J. Combinatorial Theory B 50 (1990) 198-207.

100 Embeddings of graphs with no short non-contractible cycles, J. Combinatorial
Theory B 48 (1990) 155-177.

101 A link between the Jordan curve theorem and the Kuratowski planarity
criterion, Amer. Math. Monthly 97 (1990) 216-218.

102 Large a -preserving sets in infinite a-connected graphs,
in: A Tribute to Paul Erdös (ed. A. Baker, B. Bollobás, and
A. Hajnal),

Cambridge University Press 1990,
pp. 445-450.

103 (with M.O. Albertson, D.M. Berman, and J. Hutchinson) Graphs with
homeomorphically irreducible spanning trees, J. Graph

Theory 14 (1990) 247-258.

104 (with J. Gimbel) Partial orders on a fixed graph, in: Contemporary
Methods in Graph Theory (ed. R. Bodendiek),

Wissenschaftsverlag, Mannheim 1990,
pp. 305-311.

105 Recent results on graph embeddings, in: Graph Theory, Combinatorics,
and Applications (Y. Alavi, G. Chartrand, O.R. Ollerman,

A.J. Schwenk, eds.), John Wiley
and Sons (1991), pp. 1093-1103.

106 Highly connected non-2-linked digraphs, Combinatorica 11 (1991)
393-395.

107 Tilings of the torus and the Klein bottle and vertex-transitive
graphs on a fixed surface, Trans. Amer. Math. Soc. 323 (1991)

605-635.

108 (with V. Petrovic) Kings in k-partite tournaments, Discrete Math.
98 (1991) 237-238.

109 Broer, skak og netværk (in Danish), Naturens Verden (1992)
388-393.

110 Trees, ends, and transience, in: Harmonic Analysis and Discrete
Potential Theory (M.A. Picardello, ed.), Plenum Press, New York (1992)
pp. 259-266.

111 The Jordan-Schönfliess theorem and the classification of surfaces,
Amer. Math. Mothly 99 (1992) 116-130.

112 (with S. Markvorsen and S. McGuinness) Transient random walks on
graphs and metric spaces with applications to hyperbolic

surfaces, Proc. London Math.
Soc. 64 (1992) 1-20.

113 Isoperimetric inequalities and transient random walks on graphs,
The Ann. of Probability 20 (1992) 1592-1600.

114 (with J. Bang-Jensen) A polynomial algorithm for the 2-path problem
for semi-complete digraphs, SIAM Journal of Discrete Math.

5(1992) 366-376.

115 (with J. Bang-Jensen and Y. Manoussakis) A polynomial algorithm
for Hamiltonian connectedness in semicomplete digraphs, J.

Algorithms 13 (1992) 114-127.

116 Infinite connected graphs with no end-preserving spanning trees,
J. Combinatorial Theory B 54 (1992) 322-324.

117 The Hadwiger number of infinite vertex-transitive graphs, Combinatorica
12 (1992) 481-491.

118 The even cycle problem for directed graphs, J. Amer. Math. Soc.
5 (1992) 217-229.

119 A characterization of the 2-sphere in terms of Jordan curve separation,
Proc. Amer. Math. Soc. 115 (1992) 863-864.

120 Plane cubic graphs with prescribed face areas, Combinatorics, Probability
and Computing 1 (1992) 371-381.

121 Triangulating a surface with a prescribed graph, J. Combinatorial
Theory B 57 (1993) 196-206.

122 (with B. Richter) Minimal graphs with crossing number at least k,
J. Combinatorial Theory B 58 (1993) 217-224.

123 The even cycle problem for planar digraphs, J. Algorithms 15 (1993)
61-75.

124 (with W. Woess) Vertex-transitive graphs and accessibility, J. Combinatorial
Theory B 58 (1993) 248-268.

125 5-coloring maps on surfaces, J. Combinatorial
Theory B 59 (1993) 89-105.

126 (with A.E. Brouwer and I.J. Dejter) Highly symmetric subgraphs of
hypercubes, J. Algebraic Combinatorics 2 (1993) 25-29.

127 Trees in triangulations, J. Combinatorial Theory B 60 (1994) 56-62.

128 Five-coloring graphs on the torus, J. Combinatorial Theory B 62
(1994) 11-33.

129 Every planar graph is 5-choosable, J. Combinatorial Theory B 62
(1994) 180-181.

130 Grötzsch's theorem and its counterpart for the torus and the
projective plane, J. Combinatorial Theory B 62 (1994) 268-279.

131 Embeddings of graphs, Discrete Math. 124 (1994) 217-228.

132 (with R.B.Richter) Intersections of curve systems and the
crossing number of

C5#C5, Discrete and
Computational Geometry 13 (1995) 149-159.

133 3-list-coloring planar graphs of girth 5,
J.Combinatorial Theory B 64 (1995) 101-107.

134 Decomposing a planar graph into degenerate graphs, J. Combinatorial
Theory B 65 (l995) 305-314.

135 Embeddings and minors, in: Handbook of Combinatorics (eds. M. Grötschel,
L. Lovász, and R. Graham), North-Holland 1995

pp 302-349.

136 Directed cycles with two chords and strong spanning directed
subgraphs with few arcs, J.Combinatorial Theory B66 (1996) 24-33.

137 K5-subdivisions in graphs, Combinatorics, Probability
and Computing 5 (1996) 179-189.

138 On the number of hamiltonian cycles in bipartite graphs,
Combinatorics, Probability and Computing 5 (1996) 437-442.

139 (with R.B.Richter) Relations between crossing numbers
of complete graphs and complete bipartite graphs, Amer. Math.

Monthly 104 (1997)
131-137.

140 The genus problem for cubic graphs, J. Combinatorial
Thoery B 69 (1997) 52-58.

141 Dirac’s conjecture on K5-subdivisions, Discrete Math.
165/166 (1997) 607-608.

142 Color-critical graphs on a fixed surface, J.Combinatorial
Theory B 70 (1997) 67-100.

143 A simpler proof of the excluded minor theorem
for higher surfaces, J.Combinatorial Theory B 70 (1997) 306-311.

144 (with R.E.L.Aldred) On the number of cycles
in 3-connected cubic graphs, J.Combinatorial Theory B 71 (1997) 79-84.

145 The zero-free intervals for chromatic polynomials
of graphs, Combinatorics Probability and Computing 6 (1997) 497-506.

146 Chords of longest cycles in cubic graphs,
J.Combinatorial Theory B 71 (1997) 211-214.

147 On the complexity of finding a minimum cycle
cover of a graph, SIAM Journal of Computing, 26 (1997) 675-677.

148 (with J.Gimbel) Coloring graphs with
fixed genus and girth, Trans. Am. Math. Soc. 349 (1997) 4555-4564.

149 (with P.Hjorth, P.Lisonek, and S.Markvorsen)
Finite metric spaces of strictly negative type, Linear Algebra and its

Applications,
270 (1998) 255-273.

150 Independent dominating sets and a second Hamiltonian
cycle in regular graphs, J.Combinatorial Theory B 72 (1998) 104-109.

151 (with R.Diestel, T.R.Jensen, and K.Y.Gorbunov)
Highly connected sets and the excluded grid theorem, J.Combinatorial

Theory
B 75 (1999) 61-73.

152 Two-coloring the edges of a cubic graph such that
each monochromatic component is a path of length at most 5,

J.Combinatorial
Theory B 75 (1999) 100-109.

153 Parity, cycle space, and K4-subdivisions in graphs,
in:Surveys in Combinatorics 1999 (eds. J.D.Lamb and D.A.Preece)

London Math.
Soc. Lecture Note Ser. 267, Cambridge University Press, Cambridge 1999,
pp 223-237.

154 On the Nelson unit distance coloring problem,
Amer. Math. Monthly 106 (1999) 850-853.

155 The rendezvous number of a symmetric matrix and
a compact metric space, Amer. Math. Monthly 107 (2000) 163-166.

156 (with T.R.Jensen) The color space of a graph,
J.Graph Theory 34 (2000) 234-245.

157 (with J.Gimbel) Coloring triangle-free
graphs with fixed size, Discrete Math. 219 (2000) 275-277.

158 Chromatic roots and hamiltonian paths, J.Combinatorial
Theory B 80 (2000) 218-224.

159 The Erdos-Posa property for odd cycles in graphs of
large connectivity, Combinatorica Special Issue:
Paul Erdos and his Mathematics, 21 (2001) 321-333.

160 Totally odd K4-subdivisions in 4-chromatic graphs,
Combinatorica 21 (2001) 217-443.

161 Decomposing a planar graph into an independent set and a
3-degenerate graph, J.Combinatorial Theory B 83 (2001) 262-271.

162 Chromatic graph theory, in : Challenges for the 21th Century,
International Conference on Fundamental Sciences: Mathematics and Theoretical
Physics, (L.H.Y. Chen, J.P.Jesudason, C.H.Lai, C.H.Oh, K.K.Phua, and E.-C.Tan,
eds) World ScientificPubl. Co., Singapore (2001) 183-195.

163 (Monograph with B. Mohar) Graphs on Surfaces, Johns Hopkins University Press,
Baltimore 2001.

164 (with T. Bohme and B. Mohar) Long cycles in graphs on a fixed surface,
J.Combinatorial Theory B 85 (2002) 338-347.

165 (with R.B.Richter) 3-connected planar spaces uniquely embed in the sphere,
Trans. Amer. Math. Soc. 354 (2002) 4585-4595.

166 An intersection graph of straight lines, Discrete Math. 259 (2002) 359-360.

167 On the chromatic number of triangle-free graphs of large minimum degree,
Combinatorica 22 (2002) 591-596.

168 The chromatic number of a graph of girth 5 on a fixed surface,
J.Combinatorial Theory B 87 (2003) 38-71.

169 A short list color proof of Grotzsch's theorem, J.Combinatorial Theory B 88
(2003) 189-192.

170 Tutte's spring theorem, J.Graph Theory 45 (2004) 272-280.

171 Quadrangulations and 4-color-critical graphs, J.Combinatorial Theory B 91
(2004) 147-149.

172 (with R.E.L.Aldred) Graphs with not all possible path-kernels, Discrete Math.
285 (2004) 297-300.

173 The locally connected compact metric spaces embeddable in the plane,
Combinatorica 24 (2004) 699-718.

174 Some remarks on Hajos' conjecture,
J.Combinatorial Theory B 93 (2005) 95-105.

175 Classification of locally 2-connected compact metric spaces, Combinatorica
25 (2005) 85-103.

176 (with V.Petrovic) Edge-disjoint Hamiltonian cycles in hypertournaments,
J.Graph Theory 51 (2006) 49-52.

177 (with R.Diestel) A Cantor-Bernstein theorem for paths in graphs, Amer. Math. Monthly
113 (2006) 161-165.

178 (with A.Bondy, J.Shen, S.Thomasse´) Density conditions for
triangles in multipartite graphs, Combinatorica 26 (2006) 121-131.

179 (with J.Barat) Claw-decompositions and Tutte-orientation, J.Graph Theory
52 (2006) 135-146.

180 Rectangular and visibility representations of infinite planar graphs, J.Graph Theory
52 (2006) 257-265.

181 The number of k-colorings of a graph on a fixed surface, Discrete Math.306
(2006) 3145-3153.

182 On the max-cut problem for a planar, cubic, triangle-free graph, and the
Chinese postman problem for a planar triangulation, J.Graph Theory 53 (2006)
261-269.

183 Hajós' conjecture for line graphs, J.Combinatorial Theory B 97 (2007)
156-157.

184 On the chromatic number of pentagon-free graphs of large minimum degree,
Combinatorica 27 (2007) 241-243.

185 Many 3-colorings of triangle-free planar graphs, J.Combinatorial Theory B
97 (2007) 334-349.

186 Exponentially many 5-list-colorings of planar graphs, J.Combinatorial Theory B
97 (2007) 571-583.

187 Decompositions of highly connected graphs into paths
of length 3, J.Graph Theory
58 (2008) 286-292.

188 (with A.Vella) Graph-like continua, augmenting arcs, and Menger's theorem, Combinatorica
28 (2008) 595-623.

189.
2-list-coloring planar
graphs
without monochromatic triangles, J.Combinatorial Theory B
98 (2008) 1337-1348.

190. Edge-decompositions of highly connected graphs, Abh. Math. Semin. Univ.
Hamburg 18 (2008) 17-26.

191. (with R.E.L. Aldred) On the maximum number of cycles
in a planar graph, J. Graph Theory 53 (2008) 255-264.

192. The chromatic polynomial and list clorings, J.Combinatorial Theory B 99
(2009) 474-479.

193. (with K.Kawarabayashi) Decomposing a planar graph of girth $5$ into an
independent set

and a forest , J.Combinatorial Theory B 99 (2009) 674-684.

194. Spanning trees and orientations of graphs,
J.Combinatorics 1 (2010) 101-111.

195.
(with
M.R. Fellows, F.V. Fomin, D.
Lokshtanov, F.
Rosamond, S. Saurabh, S. Szeider)
On the complexity of some
colorful problems parameterized by treewidth,
Information
and Computation 209 (2011) 143–153.

196 (with
M.Alishahi and A.Taherkhani) Rainbow paths with prescribed ends, Electronic J.
Combinatorics 18 (2011), #P86.

197 (with
A.Kündgen and G.Leander) Switchings, extensions, and reductions in central
digraphs, J.Combinatorial Theory A 118 (2011) 2025-2034.

198 (with R.B.Richter and B.Rooney) On planarity of compact, locally
connected metric spaces, Combinatorica 31 (2011) 365-376.

199 (with G.L.Chia) Grinberg's criterion applied to some non-planar graphs,
Ars Combinatoria 100 (2011) 3-7.

200 (with G.L.Chia) On the number
of longest and almost longest cycles in cubic graphs,
Ars Combinatoria 104 (2012) 307-320.

201 The weak 3-flow conjecture and
the weak circular flow conjecture, J.Combinatorial Theory B 102 (2012) 521-529.

202 (with K.Kawarabayashi) From
the plane to higher surfaces , J.Combinatorial Theory B 102 (2012) 852-868.

203 (with
A. Alahmadia,
R.E.L. Aldred, R.
dela Cruz,
P. Solé)
The
maximum number of minimal codewords in long codes

207 (with L.M.
Lóvász, Y. Wu, C-Q. Zhang) Nowhere-zero 3-flows and Z3-connectivity for
6-edge-connected graphs. J.Combinatorial Theory B 103 (2013) 587-598.

209. Group flow, complex flow, unit vector flow, and the (2 + epsilon)- flow conjecture J.Combinatorial Theory B 108 (2014) 81-91.