University of Cambridge > Talks.cam > Combinatorics Seminar > Planar graphs: One graph to rule them all

Planar graphs: One graph to rule them all

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  • UserMarthe Bonamy (University of Bordeaux)
  • ClockThursday 24 October 2019, 14:30-15:30
  • HouseMR12.

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

Consider all planar graphs on n vertices. What is the smallest graph that contains them all as induced subgraphs? We provide an explicit construction of such a graph on n(4/3+o(1)) vertices, which improves upon the previous best upper bound of n(2+o(1)), obtained in 2007 by Gavoille and Labourel.

In this talk, we will gently introduce the audience to the notion of so-called universal graphs (graphs containing all graphs of a given family as induced subgraphs), and devote some time to a key lemma in the proof. That lemma comes from a recent breakthrough by Dujmovińá, Joret, Micek, Morin, Ueckerdt and Wood regarding the structure of planar graphs, and has already many interesting consequences – we hope the audience will be able to derive more. This is based on joint work with Cyril Gavoille and Michal Pilipczuk.

This talk is part of the Combinatorics Seminar series.

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