On the degree-chromatic polynomial of a tree

Diego Cifuentes (1)

1 UNIANDES - Departamento de Matematicas [Univ de los Andes Colombia]

The degree chromatic polynomial $P_m(G,k)$ of a graph $G$ counts the number of $k$ -colorings in which no vertex has m adjacent vertices of its same color. We prove Humpert and Martin's conjecture on the leading terms of the degree chromatic polynomial of a tree.

Le polynôme degré chromatique $P_m(G,k)$ d'un graphe $G$ compte le nombre de $k$-colorations dans lesquelles aucun sommet n'a m sommets adjacents de sa même couleur. On démontre la conjecture de Humpert et Martin sur les coefficients principaux du polynôme degré chromatique d'un arbre.

Mots clés: chromatic polynomial; graph coloring; tree

Domaines: Mathématique discrète [cs.DM]

Diego Cifuentes. On the degree-chromatic polynomial of a tree. 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), 2012, Nagoya, Japan. pp.69-72, ⟨10.46298/dmtcs.3020⟩. ⟨hal-01283152⟩