k-tuple chromatic number of the cartesian product of graphs
Identifieur interne : 000872 ( Main/Exploration ); précédent : 000871; suivant : 000873k-tuple chromatic number of the cartesian product of graphs
Auteurs : Flavia Bonomo [Argentine] ; Ivo Koch [Argentine] ; Pablo Torres [Argentine] ; Mario Valencia-Pabon [France]Source :
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Abstract
A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two vertices are adjacent, the corresponding sets of colors are disjoint. The k-tuple chromatic number of G, χ k (G), is the smallest t so that there is a k-tuple coloring of G using t colors. It is well known that χ(GH) = max{χ(G), χ(H)}. In this paper, we show that there exist graphs G and H such that χ k (GH) > max{χ k (G), χ k (H)} for k ≥ 2. Moreover, we also show that there exist graph families such that, for any k ≥ 1, the k-tuple chromatic number of their cartesian product is equal to the maximum k-tuple chromatic number of its factors.
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The k-tuple chromatic number of G, χ k (G), is the smallest t so that there is a k-tuple coloring of G using t colors. It is well known that χ(GH) = max{χ(G), χ(H)}. In this paper, we show that there exist graphs G and H such that χ k (GH) > max{χ k (G), χ k (H)} for k ≥ 2. Moreover, we also show that there exist graph families such that, for any k ≥ 1, the k-tuple chromatic number of their cartesian product is equal to the maximum k-tuple chromatic number of its factors.</div></front></TEI><affiliations><list><country><li>Argentine</li><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Metz</li><li>Nancy</li></settlement><orgName><li>Université de Lorraine</li></orgName></list><tree><country name="Argentine"><noRegion><name sortKey="Bonomo, Flavia" sort="Bonomo, Flavia" uniqKey="Bonomo F" first="Flavia" last="Bonomo">Flavia Bonomo</name></noRegion><name sortKey="Koch, Ivo" sort="Koch, Ivo" uniqKey="Koch I" first="Ivo" last="Koch">Ivo Koch</name><name sortKey="Torres, Pablo" sort="Torres, Pablo" uniqKey="Torres P" first="Pablo" last="Torres">Pablo Torres</name></country><country name="France"><region name="Grand Est"><name sortKey="Valencia Pabon, Mario" sort="Valencia Pabon, Mario" uniqKey="Valencia Pabon M" first="Mario" last="Valencia-Pabon">Mario Valencia-Pabon</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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