Separating tree-chromatic number from path-chromatic number

Abstract 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.

[1]  J. Spencer.  Ramsey Theory , 1990 .

[2]  Tony Huynh,et al.  Tree‐Chromatic Number Is Not Equal to Path‐Chromatic Number* , 2015, J. Graph Theory.

[3]  P. Erdös,et al.  Graph Theory and Probability , 1959 .

[4]  Paul D. Seymour,et al.  Tree-chromatic number , 2016, J. Comb. Theory, Ser. B.

[5]  Keith R. Milliken,et al.  A Ramsey Theorem for Trees , 1979, J. Comb. Theory, Ser. A.