Geodesic
A note on edge-colourings avoiding rainbow \(K_{4}\) and monochromatic \(K_{m}\)
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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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 $maxR(n,{K_m},{K_4}) \leq n^{3/2}\sqrt{2m}$ for all $m\geq 3$. 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.
DOI : 10.37236/257
Classification : 05C55, 05C15
Mots-clés : mixed Ramsey number, incidence graphs of finite projective planes 
@article{10_37236_257,
     author = {Veselin Jungi\'c and Tom\'a\v{s} Kaiser and Daniel Kr\'al'},
     title = {A note on edge-colourings avoiding rainbow {\(K_{4}\)} and monochromatic {\(K_{m}\)}},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/257},
     zbl = {1230.05206},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/257/}
}
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Veselin Jungić; Tomáš Kaiser; Daniel Král'. A note on edge-colourings avoiding rainbow \(K_{4}\) and monochromatic \(K_{m}\). The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/257

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