Incidence Choosability of Graphs

Brahim Benmedjdoub (1) , Isma Bouchemakh (1) , Eric Sopena (2) , ´ Eric Sopena

1 L'IFORCE - L'IFORCE
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

An incidence of a graph G is a pair (v, e) where v is a vertex of G and e is an edge of G incident with v. Two incidences (v, e) and (w, f) of G are adjacent whenever (i) v = w, or (ii) e = f , or (iii) vw = e or f. An incidence p-colouring of G is a mapping from the set of incidences of G to the set of colours {1,. .. , p} such that every two adjacent incidences receive distinct colours. Incidence colouring has been introduced by Brualdi and Quinn Massey in 1993 and, since then, studied by several authors. In this paper, we introduce and study the list version of incidence colouring. We determine the exact value of – or upper bounds on – the incidence choice number of several classes of graphs, namely square grids, Halin graphs, cactuses and Hamiltonian cubic graphs.

Mots clés: Incidence colouring; Incidence list colouring; List colouring; Square grid; Halin graph; Hamiltonian cubic graph; Hamiltonian cubic graph MSC 2010: 05C15

Domaines: Mathématique discrète [cs.DM]

Brahim Benmedjdoub, Isma Bouchemakh, Eric Sopena, ´ Eric Sopena. Incidence Choosability of Graphs. 2017. ⟨hal-01517863v2⟩