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» On Lengths of Rainbow Cycles
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DM
2007
116views more  DM 2007»
13 years 9 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»
13 years 9 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»
13 years 9 months ago
Cycle lengths in sparse graphs
Benny Sudakov, Jacques Verstraëte
DM
2010
131views more  DM 2010»
13 years 9 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...