Graphs with full rank 3-color matrix and few 3-colorings

Sergey Norine (1) , Jean-Sébastien Sereni (2, 3)

1 Department of Mathematics - Princeton University
2 KAM - Department of Applied Mathematics (KAM)
3 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

We exhibit a counterexample to a conjecture of Thomassen stating that the number of distinct 3-colorings of every graph whose 3-color matrix has full column rank is superpolynomial in the number of vertices.

Mots clés: Graph; Vertex coloring; Vector space

Domaines: Mathématique discrète [cs.DM]

Sergey Norine, Jean-Sébastien Sereni. Graphs with full rank 3-color matrix and few 3-colorings. Journal of Combinatorial Theory, Series B, 2008, 98 (5), pp.1115--1116. ⟨10.1016/j.jctb.2007.12.001⟩. ⟨hal-00487281⟩