The incidence chromatic number of toroidal grids
Éric Sopena, Jiaojiao Wu · Discussiones Mathematicae Graph Theory · 2012
An incidence in a graph G is a pair (v, e) with v ∈ V (G) and e ∈ E(G), such that v and e are incident.Two incidences (v, e) and (w, f ) are adjacent if v = w, or e = f , or the edge vw equals e or f .The incidence chromatic number of G is the smallest k for which there exists a mapping from the set of incidences of G to a set of k colors that assigns distinct colors to adjacent incidences.In this paper, we prove that the incidence chromatic number of the toroidal grid T m,n = C m 2C n equals 5 when m, n ≡ 0 (mod 5) and 6 otherwise.