k-tuple colorings of the Cartesian product of graphs

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, χk(G), is the smallest t so that there is a k-tuple coloring of G using t colors. It is well known t...

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Detalles Bibliográficos
Autores principales:	Bonomo, Flavia, Koch, Ivo
Publicado:	2017
Materias:	Cartesian product of graphs Cayley graphs Hom-idempotent graphs k-tuple colorings Kneser graphs Color Graphic methods Set theory Cartesian Products Chromatic number Graph G Idempotent Kneser graph Graph theory
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0166218X_v245_n_p177_Bonomo http://hdl.handle.net/20.500.12110/paper_0166218X_v245_n_p177_Bonomo
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_0166218X_v245_n_p177_Bonomo
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spelling	paper:paper_0166218X_v245_n_p177_Bonomo2023-06-08T15:15:36Z k-tuple colorings of the Cartesian product of graphs Bonomo, Flavia Koch, Ivo Cartesian product of graphs Cayley graphs Hom-idempotent graphs k-tuple colorings Kneser graphs Color Graphic methods Set theory Cartesian product of graphs Cartesian Products Cayley graphs Chromatic number Graph G Idempotent Kneser graph Graph theory 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, χk(G), is the smallest t so that there is a k-tuple coloring of G using t colors. It is well known that χ(G□H)=max{χ(G),χ(H)}. In this paper, we show that there exist graphs G and H such that χk(G□H)>max{χk(G),χk(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. © 2017 Elsevier B.V. Fil:Bonomo, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Koch, I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0166218X_v245_n_p177_Bonomo http://hdl.handle.net/20.500.12110/paper_0166218X_v245_n_p177_Bonomo
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Cartesian product of graphs Cayley graphs Hom-idempotent graphs k-tuple colorings Kneser graphs Color Graphic methods Set theory Cartesian product of graphs Cartesian Products Cayley graphs Chromatic number Graph G Idempotent Kneser graph Graph theory
spellingShingle	Cartesian product of graphs Cayley graphs Hom-idempotent graphs k-tuple colorings Kneser graphs Color Graphic methods Set theory Cartesian product of graphs Cartesian Products Cayley graphs Chromatic number Graph G Idempotent Kneser graph Graph theory Bonomo, Flavia Koch, Ivo k-tuple colorings of the Cartesian product of graphs
topic_facet	Cartesian product of graphs Cayley graphs Hom-idempotent graphs k-tuple colorings Kneser graphs Color Graphic methods Set theory Cartesian product of graphs Cartesian Products Cayley graphs Chromatic number Graph G Idempotent Kneser graph Graph theory
description	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, χk(G), is the smallest t so that there is a k-tuple coloring of G using t colors. It is well known that χ(G□H)=max{χ(G),χ(H)}. In this paper, we show that there exist graphs G and H such that χk(G□H)>max{χk(G),χk(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. © 2017 Elsevier B.V.
author	Bonomo, Flavia Koch, Ivo
author_facet	Bonomo, Flavia Koch, Ivo
author_sort	Bonomo, Flavia
title	k-tuple colorings of the Cartesian product of graphs
title_short	k-tuple colorings of the Cartesian product of graphs
title_full	k-tuple colorings of the Cartesian product of graphs
title_fullStr	k-tuple colorings of the Cartesian product of graphs
title_full_unstemmed	k-tuple colorings of the Cartesian product of graphs
title_sort	k-tuple colorings of the cartesian product of graphs
publishDate	2017
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0166218X_v245_n_p177_Bonomo http://hdl.handle.net/20.500.12110/paper_0166218X_v245_n_p177_Bonomo
work_keys_str_mv	AT bonomoflavia ktuplecoloringsofthecartesianproductofgraphs AT kochivo ktuplecoloringsofthecartesianproductofgraphs
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k-tuple colorings of the Cartesian product of graphs

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