Given graphs G,H, is it possible to find a matching which, when deleted from G, destroys all copies of H? The answer is obvious for some inputs—notably, when G is a large complete graph the answer is “no”—but in general this can be a very difficult question. In this thesis, we study this decision problem when H is a fixed tree or cycle; our aim is to identify those H for which it can be solved efficiently.
The H-transverse matching problem, TM(H) for short, asks whether an input graph admits a matching M such that no subgraph of G − M is isomorphic to H. The main goal of this thesis is the following dichotomy. When H is a triangle or one of a few small-diameter trees, there is a polynomial-time algorithm to find an H-transverse matching if one exists. However, TM(H) is NP-complete when H is any longer cycle or a tree of diameter ≥ 4. In addition, we study the restriction of these problems to structured graph classes. / Graduate
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/4137 |
| Date | 20 August 2012 |
| Creators | Churchley, Ross William |
| Contributors | Huang, Jing |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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