Maximum K-vertex covers for some classes of graphs.

Abstract

Leung Chi Wai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 52-57).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivations --- p.1Chapter 1.2 --- Related work --- p.3Chapter 1.2.1 --- Fixed-parameter tractability --- p.3Chapter 1.2.2 --- Maximum k-vertex cover --- p.4Chapter 1.2.3 --- Dominating set --- p.4Chapter 1.3 --- Overview of the thesis --- p.5Chapter 2 --- Preliminaries --- p.6Chapter 2.1 --- Notation and definitions --- p.6Chapter 2.1.1 --- Basic definitions --- p.6Chapter 2.1.2 --- Partial t-trees --- p.7Chapter 2.1.3 --- Cographs --- p.9Chapter 2.1.4 --- Chordal graphs and interval graphs --- p.11Chapter 2.2 --- Upper bound --- p.12Chapter 2.3 --- Extension method --- p.14Chapter 3 --- Planar Graphs --- p.17Chapter 3.1 --- Trees --- p.17Chapter 3.2 --- Partial t-trees --- p.23Chapter 3.3 --- Planar graphs --- p.30Chapter 4 --- Perfect Graphs --- p.34Chapter 4.1 --- Maximum k-vertex cover in cographs --- p.34Chapter 4.2 --- Maximum dominating k-set in interval graphs --- p.39Chapter 4.3 --- Maximum k-vertex subgraph in chordal graphs --- p.46Chapter 4.3.1 --- Maximum k-vertex subgraph in partial t- trees --- p.46Chapter 4.3.2 --- Maximum k-vertex subgraph in chordal graphs --- p.47Chapter 5 --- Concluding Remarks --- p.49Chapter 5.1 --- Summary of results --- p.49Chapter 5.2 --- Open problems --- p.5