Title:
Extremal Functions for Contractions of Graphs
Extremal Functions for Contractions of Graphs
| dc.contributor.advisor | Thomas, Robin | |
| dc.contributor.author | Song, Zixia | en_US |
| dc.contributor.committeeMember | Richard Duke | |
| dc.contributor.committeeMember | Robert G. Parker | |
| dc.contributor.committeeMember | Anurag Singh | |
| dc.contributor.committeeMember | William T. Trotter | |
| dc.contributor.department | Algorithms, Combinatorics, and Optimization | en_US |
| dc.contributor.department | Mathematics | |
| dc.date.accessioned | 2005-06-16T20:10:06Z | |
| dc.date.available | 2005-06-16T20:10:06Z | |
| dc.date.issued | 2004-07-08 | en_US |
| dc.description.abstract | In this dissertation, a problem related to Hadwiger's conjecture has been studied. We first proved a conjecture of Jakobsen from 1983 which states that every simple graphs on $n$ vertices and at least (11n-35)/2 edges either has a minor isomorphic to K_8 with one edge deleted or is isomorphic to a graph obtained from disjoint copies of K_{1, 2, 2, 2, 2} and/or K_7 by identifying cliques of size five. We then studied the extremal functions for complete minors. We proved that every simple graph on nge9 vertices and at least 7n-27 edges either has a minor, or is isomorphic to K_{2, 2, 2, 3, 3}, or is isomorphic to a graph obtained from disjoint copies of K_{1, 2, 2, 2, 2, 2} by identifying cliques of size six. This result extends Mader's theorem on the extremal function for K_p minors, where ple7. We discussed the possibilities of extending our methods to K_{10} and K_{11} minors. We have also found the extremal function for K_7 plus a vertex minor. | en_US |
| dc.description.degree | Ph.D. | en_US |
| dc.format.extent | 549703 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1853/6425 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Georgia Institute of Technology | en_US |
| dc.subject | Graph minors | en_US |
| dc.subject | Graph | en_US |
| dc.subject | Hadwiger's conjecture | en_US |
| dc.subject | 4-color theorem | en_US |
| dc.subject | Linkage | en_US |
| dc.subject | Cockade | en_US |
| dc.subject.lcsh | Graph theory | en_US |
| dc.subject.lcsh | Extremal problems (Mathematics) | en_US |
| dc.title | Extremal Functions for Contractions of Graphs | en_US |
| dc.type | Text | |
| dc.type.genre | Dissertation | |
| dspace.entity.type | Publication | |
| local.contributor.corporatename | College of Sciences | |
| local.contributor.corporatename | School of Mathematics | |
| relation.isOrgUnitOfPublication | 85042be6-2d68-4e07-b384-e1f908fae48a | |
| relation.isOrgUnitOfPublication | 84e5d930-8c17-4e24-96cc-63f5ab63da69 |
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