On the game chromatic number of Cartesian product of graphs

The game chromatic number refers to the smallest integer k such that the first player Alice is assumed of a victory in the coloring game variety wherein Alice and Bob take turns in coloring vertices of a graph, with the only rule that adjacent vertices cannot have the same color. Alice wins if all v...

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Main Authors: Encinas, Sarah Jane K., Yuson, Berlyn Grace C.
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Language:English
Published: Animo Repository 2010
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Online Access:https://animorepository.dlsu.edu.ph/etd_bachelors/5343
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Institution: De La Salle University
Language: English
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spelling oai:animorepository.dlsu.edu.ph:etd_bachelors-57712022-03-11T07:14:13Z On the game chromatic number of Cartesian product of graphs Encinas, Sarah Jane K. Yuson, Berlyn Grace C. The game chromatic number refers to the smallest integer k such that the first player Alice is assumed of a victory in the coloring game variety wherein Alice and Bob take turns in coloring vertices of a graph, with the only rule that adjacent vertices cannot have the same color. Alice wins if all vertices have been colored. Otherwise, Bob wins. This thesis provides the proofs for the game chromatic number of special classes of graphs which includes paths, cycles, complete graphs, complete bipartite graphs and complete bipartite-1-factor graphs, communicated by Professor Kiyoshi Ando of the University of Electrocommunications, Tokyo, Japan. The game chromatic number of the Cartesian product of graphs, specifically the product of a complete graph of order 2 with a path, a cycle and a complete graph were also discussed based on the paper Game chromatic number of Cartesian product graphs written by T. Bartnicki, B. Bresar, J. Grytczuk, M. Kovse, Z. Miechowics and I. Peterin, published on May 12, 2008 on The Electronic Journal of Combinatorics. 2010-01-01T08:00:00Z text https://animorepository.dlsu.edu.ph/etd_bachelors/5343 Bachelor's Theses English Animo Repository Graph theory Graph coloring Mathematics
institution De La Salle University
building De La Salle University Library
continent Asia
country Philippines
Philippines
content_provider De La Salle University Library
collection DLSU Institutional Repository
language English
topic Graph theory
Graph coloring
Mathematics
spellingShingle Graph theory
Graph coloring
Mathematics
Encinas, Sarah Jane K.
Yuson, Berlyn Grace C.
On the game chromatic number of Cartesian product of graphs
description The game chromatic number refers to the smallest integer k such that the first player Alice is assumed of a victory in the coloring game variety wherein Alice and Bob take turns in coloring vertices of a graph, with the only rule that adjacent vertices cannot have the same color. Alice wins if all vertices have been colored. Otherwise, Bob wins. This thesis provides the proofs for the game chromatic number of special classes of graphs which includes paths, cycles, complete graphs, complete bipartite graphs and complete bipartite-1-factor graphs, communicated by Professor Kiyoshi Ando of the University of Electrocommunications, Tokyo, Japan. The game chromatic number of the Cartesian product of graphs, specifically the product of a complete graph of order 2 with a path, a cycle and a complete graph were also discussed based on the paper Game chromatic number of Cartesian product graphs written by T. Bartnicki, B. Bresar, J. Grytczuk, M. Kovse, Z. Miechowics and I. Peterin, published on May 12, 2008 on The Electronic Journal of Combinatorics.
format text
author Encinas, Sarah Jane K.
Yuson, Berlyn Grace C.
author_facet Encinas, Sarah Jane K.
Yuson, Berlyn Grace C.
author_sort Encinas, Sarah Jane K.
title On the game chromatic number of Cartesian product of graphs
title_short On the game chromatic number of Cartesian product of graphs
title_full On the game chromatic number of Cartesian product of graphs
title_fullStr On the game chromatic number of Cartesian product of graphs
title_full_unstemmed On the game chromatic number of Cartesian product of graphs
title_sort on the game chromatic number of cartesian product of graphs
publisher Animo Repository
publishDate 2010
url https://animorepository.dlsu.edu.ph/etd_bachelors/5343
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