On graph-transverse matching problems
| dc.contributor.author | Churchley, Ross William | |
| dc.contributor.supervisor | Huang, Jing | |
| dc.date.accessioned | 2012-08-20T20:11:28Z | |
| dc.date.available | 2012-08-20T20:11:28Z | |
| dc.date.copyright | 2012 | en_US |
| dc.date.issued | 2012-08-20 | |
| dc.degree.department | Dept. of Mathematics and Statistics | en_US |
| dc.degree.level | Master of Science M.Sc. | en_US |
| dc.description.abstract | 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. | en_US |
| dc.description.scholarlevel | Graduate | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/4137 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights.temp | Available to the World Wide Web | en_US |
| dc.subject | transverse matching problem | en_US |
| dc.subject | polynomial-time algorithm | en_US |
| dc.subject | complexity | en_US |
| dc.subject | NP-complete problem | en_US |
| dc.title | On graph-transverse matching problems | en_US |
| dc.type | Thesis | en_US |