Title:
Color-critical graphs on surfaces
Color-critical graphs on surfaces
| dc.contributor.advisor | Thomas, Robin | |
| dc.contributor.author | Yerger, Carl Roger, Jr. | en_US |
| dc.contributor.committeeMember | Asaf Shapira | |
| dc.contributor.committeeMember | William Cook | |
| dc.contributor.committeeMember | William T. Trotter | |
| dc.contributor.committeeMember | Yu, Xingxing | |
| dc.contributor.department | Mathematics | en_US |
| dc.date.accessioned | 2011-03-04T20:22:16Z | |
| dc.date.available | 2011-03-04T20:22:16Z | |
| dc.date.issued | 2010-08-23 | en_US |
| dc.description.abstract | A graph is (t+1)-critical if it is not t-colorable, but every proper subgraph is. In this thesis, we study the structure of critical graphs on higher surfaces. One major result in this area is Carsten Thomassen's proof that there are finitely many 6-critical graphs on a fixed surface. This proof involves a structural theorem about a precolored cycle C of length q. In general terms, he proves that a coloring, c, of C, can be extended inside the cycle, or there exists a subgraph H with at most a number of vertices exponential in q such that c can not be extended to a 5-coloring of H. In Chapter 2, we proved an alternative proof that reduces the number of vertices in H to be cubic in q. In Chapter 3, we find the nine 6-critical graphs among all graphs embeddable on the Klein bottle. In Chapter 4, we prove a result concerning critical graphs related to an analogue of Steinberg's conjecture for higher surfaces. We show that if G is a 4-critical graph embedded on surface S, with Euler genus g and has no cycles of length four through ten, then G has at most 2442g + 37 vertices. | en_US |
| dc.description.degree | Ph.D. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1853/37197 | |
| dc.publisher | Georgia Institute of Technology | en_US |
| dc.subject | Graphs | en_US |
| dc.subject | Coloring | en_US |
| dc.subject | Steinberg | en_US |
| dc.subject | Critical | en_US |
| dc.subject.lcsh | Graph theory | |
| dc.subject.lcsh | Graph coloring | |
| dc.title | Color-critical graphs on surfaces | 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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