University of Birmingham > Talks@bham > Combinatorics and Probability Seminar > Edges not in any monochromatic copy of a fixed graph

Edges not in any monochromatic copy of a fixed graph

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  • UserMaryam Sharifzadeh (Warwick)
  • ClockThursday 16 March 2017, 15:00-16:00
  • HouseLTC Watson.

If you have a question about this talk, please contact Dr Andrew Treglown.

For a family of fixed graphs H_1,...,H_k, denote by f(n;H_1,..., H_k) the maximum number of edges not contained in any monochromatic copy of H_i in colour i, in a k-edge-colouring of K_n. It is easy to see that $f(n;H,H)\ge\ex(n,H)$. In this talk, we introduce a new variant of Ramsey number, which determines f(n;H_1,..., H_k) asymptotically for non-bipartite graphs H_i. For the 3-colour case, an exact result is obtained for a subfamily of colour-critical graphs, including cliques. The special case f(n;K_3,K_3,K_3) answers a question of Ma affirmatively.

For bipartite graphs, Keevash and Sudakov showed $f(n;C_4,C_4)=\ex(n,C_4)$; recently Ma extended their result to an infinite family of bipartite graphs. We provide a larger family of bipartite graphs for which $f(n;H,H)=\ex(n,H)$. For general bipartite graphs, we prove an upper bound with an additive error term, i.e. $f(n;H,H)\le \ex(n,H)+O(1)$.

This talk is part of the Combinatorics and Probability Seminar series.

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