Title:
Special TK5 in graphs containing K4-
Special TK5 in graphs containing K4-
| dc.contributor.advisor | Yu, Xingxing | |
| dc.contributor.author | He, Dawei | |
| dc.contributor.committeeMember | Thomas, Robin | |
| dc.contributor.committeeMember | Trotter, William | |
| dc.contributor.committeeMember | Blekhermann, Greg | |
| dc.contributor.committeeMember | Li, Geoffrey Ye | |
| dc.contributor.department | Mathematics | |
| dc.date.accessioned | 2017-06-07T17:47:36Z | |
| dc.date.available | 2017-06-07T17:47:36Z | |
| dc.date.created | 2017-05 | |
| dc.date.issued | 2017-04-05 | |
| dc.date.submitted | May 2017 | |
| dc.date.updated | 2017-06-07T17:47:36Z | |
| dc.description.abstract | Given a graph K, TK is used to denote a subdivision of K, which is a graph obtained from K by substituting some edges for paths. The well-known Kelmans-Seymour conjecture states that every nonplanar 5-connected graph contains TK5 . Ma and Yu proved the conjecture for graphs containing K4-. In this dissertation, we strengthen their result in two ways. The results will be useful for completely resolving the Kelmans-Seymour conjecture. Let G be a 5-connected nonplanar graph and let x1, x2, y1, y2 in V(G) be distinct, such that G[{x1, x2, y1, y2}] is isomorphic to K4- and y1y2 is not in E(G). We show that one of the following holds: G - y2 contains K4-, or G contains a TK5 in which y2 is not a branch vertex, or G has a special 5-separation, or for any distinct w1, w2, w3 in N(y2) - {x1, x2}, G - {y2v : v not in {x1, x2, w1, w2, w3}} contains TK5. We show that one of the following holds: G - x1 contains K4-, or G contains a TK5 in which x1 is not a branch vertex, or G contains a K4- in which x1 is of degree 2, or {x2, y1, y2} may be chosen so that for any distinct z0, z1 in N(x1) - {x2, y1, y2}, G - {x1v : v not in {z0, z1, x2, y1, y2}} contains TK5. | |
| dc.description.degree | Ph.D. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1853/58301 | |
| dc.language.iso | en_US | |
| dc.publisher | Georgia Institute of Technology | |
| dc.subject | Kelmans-Seymour conjecture | |
| dc.subject | Subdivision of K5 | |
| dc.subject | K4- | |
| dc.subject | Branch vertex | |
| dc.title | Special TK5 in graphs containing K4- | |
| dc.type | Text | |
| dc.type.genre | Dissertation | |
| dspace.entity.type | Publication | |
| local.contributor.advisor | Yu, Xingxing | |
| local.contributor.corporatename | College of Sciences | |
| local.contributor.corporatename | School of Mathematics | |
| relation.isAdvisorOfPublication | 3b32a3b5-5417-4c47-8a35-79346368e87f | |
| relation.isOrgUnitOfPublication | 85042be6-2d68-4e07-b384-e1f908fae48a | |
| relation.isOrgUnitOfPublication | 84e5d930-8c17-4e24-96cc-63f5ab63da69 | |
| thesis.degree.level | Doctoral |