Contract grant sponsor: NSF; Contract grant Number: DMS-0968699.
An Improved Bound for Vertex Partitions by Connected Monochromatic K-Regular Graphs
Article first published online: 1 MAY 2012
© 2012 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 73, Issue 2, pages 127–145, June 2013
How to Cite
Sárközy, G. N., Selkow, S. M. and Song, F. (2013), An Improved Bound for Vertex Partitions by Connected Monochromatic K-Regular Graphs. J. Graph Theory, 73: 127–145. doi: 10.1002/jgt.21661
- Issue published online: 1 APR 2013
- Article first published online: 1 MAY 2012
- Manuscript Revised: 10 JAN 2012
- Manuscript Received: 3 FEB 2011
- vertex partitions;
- regulatory lemma
Improving a result of Sárközy 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