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


  • Contract grant sponsor: NSF; Contract grant Number: DMS-0968699.


Improving a result of Sárközy and Selkow, we show that for all integers inline image there exists a constant inline image such that if inline image and the edges of the complete graph inline image are colored with r colors then the vertex set of inline image can be partitioned into at most inline image 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