A note on edge-colourings avoiding rainbow K_4 and monochromatic K_m
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2009
- DOI:
- 10.48550/arXiv.0902.1608
- arXiv:
- arXiv:0902.1608
- Bibcode:
- 2009arXiv0902.1608J
- Keywords:
-
- Mathematics - Combinatorics;
- 05D10
- E-Print:
- Electronic J. Comb. 16, 1 (2009), N19