On the game chromatic number of Cartesian product of graphs
Date of Publication
2010
Document Type
Bachelor's Thesis
Degree Name
Bachelor of Science in Mathematics with specialization in Business Applications
Subject Categories
Mathematics
College
College of Science
Department/Unit
Mathematics and Statistics
Thesis Adviser
Yvette F. Lim
Defense Panel Chair
Arlene A. Pascasio
Defense Panel Member
Mark Anthony A. Garcia
John Vincent S. Morales
Abstract/Summary
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.
Abstract Format
html
Language
English
Format
Accession Number
TU16004
Shelf Location
Archives, The Learning Commons, 12F, Henry Sy Sr. Hall
Physical Description
vi, 52 leaves, illustrations, 28 cm.
Keywords
Graph theory; Graph coloring
Recommended Citation
Encinas, S. K., & Yuson, B. C. (2010). On the game chromatic number of Cartesian product of graphs. Retrieved from https://animorepository.dlsu.edu.ph/etd_bachelors/5343
Embargo Period
4-15-2021