A Note on Edge-Colourings Avoiding Rainbow K4 and Monochromatic Km

نویسندگان

  • Veselin Jungic
  • Tomás Kaiser
  • Daniel Král
چکیده

We study the mixed Ramsey number maxR(n,Km,Kr), defined as the maximum number of colours in an edge-colouring of the complete graph Kn, such that Kn 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,Km,K4) ≤ n3/2 √ 2m for all m ≥ 3. Further, we discuss a possible way to improve their lower bound on maxR(n,K4,K4) based on incidence graphs of finite projective planes.

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عنوان ژورنال:
  • Electr. J. Comb.

دوره 16  شماره 

صفحات  -

تاریخ انتشار 2009