Discussiones Mathematicae Graph Theory 33(2) (2013)
315-327
DOI: https://doi.org/10.7151/dmgt.1663
The Incidence Chromatic Number
of Toroidal Grids
Éric Sopena
Univ. Bordeaux, LaBRI, UMR5800, F-33400 Talence | Jiaojiao Wu
Department of Applied Mathematics |
Abstract
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 Tm,n = Cm[¯] Cn equals 5 when m,n ≡ 0 (mod 5) and 6 otherwise.
Keywords: incidence coloring, Cartesian product of cycles, toroidal grid
2010 Mathematics Subject Classification: 05C15.
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Received 23 October 1011
Revised 20 February 2012
Accepted 7 March 2012
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