An Improved Bound for Vertex Partitions by Connected Monochromatic K-Regular Graphs
Improving a result of Srkzy 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: 127145, 2013
vertex partitions regulatory lemma