A note on edge-colourings avoiding rainbow K_4 and monochromatic K_m
Combinatorics
2010-09-21 v1
Abstract
We study the mixed Ramsey number maxR(n,K_m,K_r), defined as the maximum number of colours in an edge-colouring of the complete graph K_n, such that K_n has no monochromatic complete subgraph on m vertices and no rainbow complete subgraph on r vertices. Improving an upper bound of Axenovich and Iverson, we show that maxR(n,K_m,K_4) <= n^{3/2}\sqrt{2m} for all m >= 3. Further, we discuss a possible way to improve their lower bound on maxR(n,K_4,K_4) based on incidence graphs of finite projective planes.
Keywords
Cite
@article{arxiv.0902.1608,
title = {A note on edge-colourings avoiding rainbow K_4 and monochromatic K_m},
author = {Veselin Jungic and Tomas Kaiser and Daniel Kral},
journal= {arXiv preprint arXiv:0902.1608},
year = {2010}
}