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                * Princeton Discrete Math Seminar *
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Speaker: Tung Nguyen (Oxford)

Thursday 26th February, 3:00 in Fine Hall 224.

Title: Polynomial 𝜒-boundedness for excluding the five-vertex path


We overview the recent resolution of a 1985 open problem of Gyárfás, that
chromatic number is polynomially bounded by clique number for graphs with no
induced five-vertex path. The proof introduces a chromatic density framework
involving chromatic quasirandomness and chromatic density increment, which
allows us to deduce the desired statement from the Erdős–Hajnal result for the
five-vertex path.

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