Title:
Coloring graphs with no k5-subdivision: disjoint paths in graphs
Coloring graphs with no k5-subdivision: disjoint paths in graphs
| dc.contributor.advisor | Yu, Xingxing | |
| dc.contributor.author | Xie, Qiqin | |
| dc.contributor.committeeMember | Blekherman, Grigoriy | |
| dc.contributor.committeeMember | Iliev, Plamen | |
| dc.contributor.committeeMember | Yu, Josephine | |
| dc.contributor.committeeMember | Huang, Hao | |
| dc.contributor.department | Mathematics | |
| dc.date.accessioned | 2020-05-20T16:56:55Z | |
| dc.date.available | 2020-05-20T16:56:55Z | |
| dc.date.created | 2019-05 | |
| dc.date.issued | 2019-03-27 | |
| dc.date.submitted | May 2019 | |
| dc.date.updated | 2020-05-20T16:56:55Z | |
| dc.description.abstract | The Four Color Theorem states that every planar graph is 4-colorable. Hajos conjectured that for any positive integer k, every graph containing no K_{k+1}-subdivision is k-colorable. However, Catlin disproved Hajos conjecture for k>=6. It is not hard to prove that the conjecture is true for k<=3. Hajos' conjecture remains open for k=4 and k=5. We consider a minimal counterexample to Hajos conjecture for k=4. We use Hajos graph to denote such counterexample. One important step to understand graphs containing K5-subdivisions is to solve the topological H problem. We characterize graphs with no topological H, and the characterization is used by He, Wang, and Yu to show that graph containing no K5-subdivisions is planar or has a 4-cut, establishing conjecture of Kelmans and Seymour. Besides the topological H problem, we also obtained some further structural information of Hajos graphs. | |
| dc.description.degree | Ph.D. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1853/62659 | |
| dc.language.iso | en_US | |
| dc.publisher | Georgia Institute of Technology | |
| dc.subject | Graph coloring | |
| dc.subject | Hajos conjecture | |
| dc.title | Coloring graphs with no k5-subdivision: disjoint paths in graphs | |
| 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 |