Colourings without monochromatic chains

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• Shagnik Das
• Tuesday 15 May 2018, 15:00-16:00
• Watson LTC.

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

In 1974, Erdős and Rothschild introduced a new kind of extremal problem, asking which n-vertex graph has the maximum number of monochromatic-triangle-free red/blue edge-colourings. While this original problem strengthens Mantel’s theorem, recent years have witnessed the study of the Erdős-Rothschild extension of several classic combinatorial theorems. In this talk, we seek the Erdős-Rothschild extension of Sperner’s Theorem. More precisely, we search for the set families in 2^{[n]} with the most monochromatic-k-chain-free r-colourings. Time and interest permitting, we shall present some results, sketch some proofs, and offer open problems.

This is joint work with Roman Glebov, Benny Sudakov and Tuan Tran.

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

This talk is included in these lists:

• Combinatorics and Probability seminar
• School of Mathematics events
• Watson LTC

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