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Monochromatic cycle partitions of edge-colored graphs

✍ Scribed by Gábor N. Sárközy

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
88 KB
Volume
66
Category
Article
ISSN
0364-9024

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✦ Synopsis

In this article we study the monochromatic cycle partition problem for non-complete graphs. We consider graphs with a given independence number (G) = . Generalizing a classical conjecture of Erd" os, Gyárfás and Pyber, we conjecture that if we r-color the edges of a graph G with (G) = , then the vertex set of G can be partitioned into at most r vertex disjoint monochromatic cycles. In the direction of this conjecture we show that under these conditions the vertex set of G can be partitioned into at most 25( r) 2 log( r) vertex disjoint monochromatic cycles. ᭧ 2010 Wiley

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