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

Print

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

Embargo Period

4-15-2021

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