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JGT
2010
135views more  JGT 2010»
13 years 8 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...
WG
2010
Springer
13 years 8 months ago
On the Small Cycle Transversal of Planar Graphs
We consider the problem of finding a k-edge transversal set that covers all (simple) cycles of length at most s in a planar graph, where s ≥ 3 is a constant. This problem, refe...
Ge Xia, Yong Zhang
JCT
2010
158views more  JCT 2010»
13 years 8 months ago
An asymptotic solution to the cycle decomposition problem for complete graphs
Let m1, m2, . . . , mt be a list of integers. It is shown that there exists an integer N such that for all n ≥ N, the complete graph of order n can be decomposed into edge-disjo...
Darryn E. Bryant, Daniel Horsley
GC
2002
Springer
13 years 9 months ago
A Note on Cycle Lengths in Graphs
We prove that for every c > 0 there exists a constant K = K(c) such that every graph G with n vertices and minimum degree at least cn contains a cycle of length t for every even...
Ronald J. Gould, Penny E. Haxell, A. D. Scott
JGT
2010
81views more  JGT 2010»
13 years 8 months ago
Cycles and paths in edge-colored graphs with given degrees
Sufficient degree conditions for the existence of properly edge-colored cycles and paths in edge-colored graphs, multigraphs and random graphs are inverstigated. In particular, we...
A. Abouelaoualim, Kinkar Chandra Das, Wenceslas Fe...