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» On Lengths of Rainbow Cycles
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DM
2007
116views more  DM 2007»
14 years 11 months ago
The Ramsey numbers for a cycle of length six or seven versus a clique of order seven
: For two given graphs G1 and G2, the Ramsey number R(G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G...
T. C. Edwin Cheng, Yaojun Chen, Yunqing Zhang, C. ...
ENDM
2008
114views more  ENDM 2008»
14 years 11 months ago
Strong oriented chromatic number of planar graphs without cycles of specific lengths
A strong oriented k-coloring of an oriented graph G is a homomorphism from G to H having k vertices labelled by the k elements of an abelian additive group M, such that for any p...
Mickaël Montassier, Pascal Ochem, Alexandre P...
COMBINATORICA
2008
93views more  COMBINATORICA 2008»
14 years 11 months ago
Cycle lengths in sparse graphs
Benny Sudakov, Jacques Verstraëte
DM
2010
131views more  DM 2010»
14 years 11 months ago
Planar graphs without adjacent cycles of length at most seven are 3-colorable
We prove that every planar graph in which no i-cycle is adjacent to a j-cycle whenever 3 i j 7 is 3-colorable and pose some related problems on the 3-colorability of planar grap...
Oleg V. Borodin, Mickaël Montassier, Andr&eac...
DM
2008
48views more  DM 2008»
14 years 11 months ago
Relative length of longest paths and longest cycles in triangle-free graphs
Daniël Paulusma, Kiyoshi Yoshimoto