Ho Man Lam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 51-54). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Statement of problems --- p.1 / Chapter 1.2 --- Notation and definitions --- p.3 / Chapter 1.3 --- Graph families --- p.4 / Chapter 1.4 --- Related work --- p.5 / Chapter 1.4.1 --- Graph modification problems --- p.5 / Chapter 1.4.2 --- Independent set --- p.6 / Chapter 1.5 --- Overview of the thesis --- p.7 / Chapter 2 --- Recognition of Nearly Chordal Graphs --- p.8 / Chapter 2.1 --- Critical edges not in triangles --- p.9 / Chapter 2.2 --- Critical edges in triangles --- p.10 / Chapter 2.3 --- A linear time algorithm --- p.13 / Chapter 3 --- Recognition of Almost Chordal Graphs --- p.15 / Chapter 3.1 --- Minimal separator --- p.16 / Chapter 3.2 --- "All chordless cycles passing through the minimal (x, z)-separator S" --- p.18 / Chapter 3.3 --- Algorithm for almost chordal graphs recognition --- p.22 / Chapter 3.4 --- Another approach to find a critical vertex if all chordless cycles pass through S --- p.26 / Chapter 3.5 --- A linear algorithm for all chordless cycles passing through S --- p.28 / Chapter 4 --- Maximum Independent Bases of Chordal Graphs --- p.32 / Chapter 4.1 --- Maximum independent base --- p.32 / Chapter 4.1.1 --- Finding a maximum independent set of a chordal graph . --- p.33 / Chapter 4.1.2 --- Another approach to prove the algorithm --- p.33 / Chapter 4.1.3 --- Maximum independent base --- p.34 / Chapter 4.1.4 --- Vertices in the maximum independent base --- p.36 / Chapter 4.1.5 --- A linear time algorithm --- p.38 / Chapter 4.2 --- Generating all maximum independent sets --- p.39 / Chapter 4.2.1 --- Relation between two maximum independent sets --- p.39 / Chapter 4.2.2 --- Algorithm --- p.40 / Chapter 4.3 --- Maximum induced split graph of a chordal graph --- p.43 / Chapter 4.3.1 --- Property of maximum induced split subgraph --- p.44 / Chapter 4.3.2 --- A linear time algorithm --- p.45 / Chapter 5 --- Concluding Remarks --- p.48 / Chapter 5.1 --- Summary of results --- p.48 / Chapter 5.2 --- Open problems --- p.48 / Bibliography --- p.51
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_324279 |
| Date | January 2003 |
| Contributors | Ho, Man Lam., Chinese University of Hong Kong Graduate School. Division of Computer Science and Engineering. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, vi, 54 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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