An Improved Bound for Vertex Partitions by Connected Monochromatic K‐Regular Graphs

Improving a result of Sarkozy and Selkow, we show that for all integers there exists a constant such that if and the edges of the complete graph are colored with r colors then the vertex set of can be partitioned into at most vertex disjoint connected monochromatic k-regular subgraphs and vertices. This is close to best possible. © 2012 Wiley Periodicals, Inc. J. Graph Theory 73: 127–145, 2013

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