Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, October 04, 2016, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Nina Kamcev

Anagram-free Colourings of Graphs

Answering a question of Erdős and Brown, Keränen constructed an infinite anagram-free sequence on four symbols, that is, a sequence which contains no consecutive symbols r₁r₂...r_kr_k+1...r_2k such that r_k+1...r_2k is a permutation of the block r₁...r_k. Motivated by the work of Alon, Grytczuk, Hałuszczak and Riordan, we study a natural generalisation of anagram-free sequences for graph colourings. We touch upon results for paths, trees, minor-free graphs and bounded-degree graphs. Surprisingly, there are bounded-degree graphs (such as random regular graphs) in which anagrams cannot be avoided unless we basically give each vertex a separate color.

Joint work with Tomasz Łuczak and Benny Sudakov.

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