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Article Dans Une Revue Discussiones Mathematicae Graph Theory Année : 2013

The Incidence Chromatic Number of Toroidal Grids

Résumé

An incidence in a graph $G$ is a pair $(v,e)$ with $v \in V(G)$ and $e \in E(G)$, 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 $T_{m,n}=C_m\Box C_n$ equals 5 when $m,n \equiv 0 \pmod 5$ and 6 otherwise.
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Dates et versions

hal-00406409 , version 1 (22-07-2009)
hal-00406409 , version 2 (27-09-2010)
hal-00406409 , version 3 (06-05-2012)

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Eric Sopena, Jiaojiao Wu. The Incidence Chromatic Number of Toroidal Grids. Discussiones Mathematicae Graph Theory, 2013, 33, pp.315-327. ⟨hal-00406409v3⟩

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