Partition a 3-colorable graph into a small bipartite subgraph and a large independent set

Authors

Qing Wang, University of Texas-Pan American

Date of Award

5-2011

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Computer Science

First Advisor

Dr. Yang Liu

Second Advisor

Dr. Zhixiang Chen

Third Advisor

Dr. Bin Fu

Abstract

Exact algorithms have made a little progress for the 3-coloring problem: improved from to since 1976. The best exact algorithm for the 3-coloring problem is by Beigel and Eppstein, and its analysis is very complicated. We study the parameterized 3-coloring problem: partitioning a 3-colorable graph into a bipartite subgraph and an independent set. Taking the size of the bipartite subgraph as the parameter k, we propose the first parameter algorithm of complexity . Our algorithm can solve the 3-coloring problem faster than the best exact algorithm for graphs with k ≤ 0.527n where n is the graph size. Our study of the parameterized 3-coloring problem brings new insight on studies of the 3-coloring problem. Experiments show that the parameterized algorithm is faster than the exact algorithm for graphs of small parameter k. Moreover, the running time of parameterized algorithm is not much related to edge density, while the running time of exact algorithm increases dramatically as edge density increases.

Comments

Copyright 2011 Qing Wang. All Rights Reserved.

https://www.proquest.com/dissertations-theses/partition-3-colorable-graph-into-small-bipartite/docview/875790283/se-2?accountid=7119

Granting Institution

University of Texas-Pan American