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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0166218X_v245_n_p177_Bonomo |
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todo:paper_0166218X_v245_n_p177_Bonomo2023-10-03T15:03:46Z k-tuple colorings of the Cartesian product of graphs Bonomo, F. Koch, I. Torres, P. Valencia-Pabon, M. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0166218X_v245_n_p177_Bonomo |
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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, F. Koch, I. Torres, P. Valencia-Pabon, M. 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. |
| format |
JOUR |
| author |
Bonomo, F. Koch, I. Torres, P. Valencia-Pabon, M. |
| author_facet |
Bonomo, F. Koch, I. Torres, P. Valencia-Pabon, M. |
| author_sort |
Bonomo, F. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_0166218X_v245_n_p177_Bonomo |
| work_keys_str_mv |
AT bonomof ktuplecoloringsofthecartesianproductofgraphs AT kochi ktuplecoloringsofthecartesianproductofgraphs AT torresp ktuplecoloringsofthecartesianproductofgraphs AT valenciapabonm ktuplecoloringsofthecartesianproductofgraphs |
| _version_ |
1807319787859083264 |