Separating Tree-chromatic number from Path-chromatic Number

Fidel Barrera-Cruz; Heather Smith; Libby Taylor; Piotr Micek; Stefan Felsner; Tam\'as M\'esz\'aros; William T. Trotter

arxiv: 1703.03973 · v3 · pith:7T3VPYNPnew · submitted 2017-03-11 · 🧮 math.CO

Separating Tree-chromatic number from Path-chromatic Number

Fidel Barrera-Cruz , Stefan Felsner , Tam\'as M\'esz\'aros , Piotr Micek , Heather Smith , Libby Taylor , William T. Trotter This is my paper

classification 🧮 math.CO

keywords numberpath-chromatictree-chromaticapplyfamilygraphsposedproblem

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We apply Ramsey theoretic tools to show that there is a family of graphs which have tree-chromatic number at most~$2$ while the path-chromatic number is unbounded. This resolves a problem posed by Seymour.

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Separating Tree-chromatic number from Path-chromatic Number

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