A note on edge-colourings avoiding rainbow K_4 and monochromatic K_m

Details A note on edge-colourings avoiding rainbow K_4 and monochromatic K_m A note on edge-colourings avoiding rainbow K_4 and monochromatic K_m

2009-02-10

arxiv.org/abs/0902.1608v1

Electronic J. Comb. 16, 1 (2009), N19

Mathematics

Combinatorics

Scientific paper

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.

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