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JGT
2010
152views more  JGT 2010»
12 years 11 months ago
Cycles of even lengths modulo k
Thomassen [9] conjectured that for all natural numbers k > 0 and m, every graph of minimum degree k + 1 contains a cycle of length congruent to 2m modulo k. We prove that this ...
Ajit A. Diwan
JGT
2010
109views more  JGT 2010»
12 years 11 months ago
Homomorphism-homogeneous graphs
We answer two open questions posed by Cameron and Nesetril concerning homomorphismhomogeneous graphs. In particular we show, by giving a characterization of these graphs, that ext...
Momchil Rusinov, Pascal Schweitzer
JGT
2010
84views more  JGT 2010»
13 years 2 months ago
Large classes of infinite k-cop-win graphs
While finite cop-win finite graphs possess a good structural characterization, none is known for infinite cop-win graphs. As evidence that such a characterization might not exis...
Anthony Bonato, Gena Hahn, Claude Tardif
JGT
2010
108views more  JGT 2010»
13 years 2 months ago
Hadwiger number and chromatic number for near regular degree sequences
: We consider a problem related to Hadwiger’s Conjecture. Let
Neil Robertson, Zi-Xia Song
JGT
2010
79views more  JGT 2010»
13 years 2 months ago
On Ramsey-type positional games
Beck introduced the concept of Ramsey games by studying the game versions of Ramsey and van der Waerden theorems. We contribute to this topic by investigating games corresponding ...
Jaroslav Nesetril, Tomás Valla
JGT
2010
128views more  JGT 2010»
13 years 2 months ago
On antimagic directed graphs
An antimagic labeling of an undirected graph G with n vertices and m edges is a bijection from the set of edges of G to the integers {1, . . . , m} such that all n vertex sums are...
Dan Hefetz, Torsten Mütze, Justus Schwartz
JGT
2010
135views more  JGT 2010»
13 years 2 months ago
Cycle length parities and the chromatic number
In 1966 Erd˝os and Hajnal proved that the chromatic number of graphs whose
Christian Löwenstein, Dieter Rautenbach, Ingo...
JGT
2010
113views more  JGT 2010»
13 years 2 months ago
Coloring plane graphs with independent crossings
We show that every plane graph with maximum face size four whose all faces of size four are vertex-disjoint is cyclically 5-colorable. This answers a question of Albertson whether...
Daniel Král', Ladislav Stacho