k-tuple chromatic number of the cartesian product of graphs

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [12 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01103534
Contributor : Mario Valencia <>
Submitted on : Wednesday, January 14, 2015 - 9:24:38 PM
Last modification on : Thursday, September 5, 2019 - 4:46:59 PM
Long-term archiving on : Wednesday, April 15, 2015 - 11:45:39 AM

File

cartesian-prod-multicol-ext-v0...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01103534, version 1

Citation

Flavia Bonomo, Ivo Koch, Pablo Torres, Mario Valencia-Pabon. k-tuple chromatic number of the cartesian product of graphs. 2014. ⟨hal-01103534⟩

Share

Metrics

Record views

403

Files downloads

556