Every planar graph without cycles of lengths 4 to 12 is acyclically 3-choosable

Hervé Hocquard (1) , Mickael Montassier (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

An acyclic coloring of a graph G is a coloring of its vertices such that : (i) no two adjacent vertices in G receive the same color and (ii) no bicolored cycles exist in G. A list assignment of G is a function L that assigns to each vertex v \in V (G) a list L(v) of available colors. Let G be a graph and L be a list assignment of G. The graph G is acyclically L-list colorable if there exists an acyclic coloring \phi of G such that \phi(v) \in L(v) for all v \in V (G). If G is acyclically L-list colorable for any list assignment L with |L(v)| >= k for all v \in V (G), then G is acyclically k-choosable. In this paper, we prove that every planar graph without cycles of lengths 4 to 12 is acyclically 3-choosable.

Mots clés: Acyclic choosability; Planar graphs; Forbidden cycles

Domaines: Mathématique discrète [cs.DM]

Hervé Hocquard, Mickael Montassier. Every planar graph without cycles of lengths 4 to 12 is acyclically 3-choosable. Information Processing Letters, 2009. ⟨hal-00402807⟩