Title:
Subdivisions of complete graphs
Subdivisions of complete graphs
| dc.contributor.advisor | Yu, Xingxing | |
| dc.contributor.author | Wang, Yan | |
| dc.contributor.committeeMember | Peng, Richard | |
| dc.contributor.committeeMember | Tetali, Prasad | |
| dc.contributor.committeeMember | Thomas, Robin | |
| dc.contributor.committeeMember | Warnke, Lutz | |
| dc.contributor.department | Mathematics | |
| dc.date.accessioned | 2017-08-17T18:58:19Z | |
| dc.date.available | 2017-08-17T18:58:19Z | |
| dc.date.created | 2017-08 | |
| dc.date.issued | 2017-05-23 | |
| dc.date.submitted | August 2017 | |
| dc.date.updated | 2017-08-17T18:58:19Z | |
| dc.description.abstract | A subdivision of a graph G, also known as a topological G and denoted by TG, is a graph obtained from G by replacing certain edges of G with internally vertex-disjoint paths. This dissertation studies a problem in structural graph theory regarding subdivisions of a complete graph in graphs. In this dissertation, we focus on TK_5, or subdivisions of K_5. A well known theorem of Kuratowski in 1932 states that a graph is planar if, and only if, it does not contain a subdivision of K_5 or K_{3,3}. Wagner proved in 1937 that if a graph other than K_5 does not contain any subdivision of K_{3,3} then it is planar or it admits a cut of size at most 2. Kelmans and, independently, Seymour conjectured in the 1970s that if a graph does not contain any subdivision of K_5 then it is planar or it admits a cut of size at most 4. In this dissertation, we give a proof of the Kelmans-Seymour conjecture. | |
| dc.description.degree | Ph.D. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1853/58633 | |
| dc.language.iso | en_US | |
| dc.publisher | Georgia Institute of Technology | |
| dc.subject | K5-subdivision | |
| dc.subject | Independent paths | |
| dc.subject | Separation | |
| dc.subject | Connectivity | |
| dc.subject | Discharging | |
| dc.subject | Contraction | |
| dc.title | Subdivisions of complete graphs | |
| dc.type | Text | |
| dc.type.genre | Dissertation | |
| dspace.entity.type | Publication | |
| local.contributor.advisor | Yu, Xingxing | |
| local.contributor.author | Wang, Yan | |
| local.contributor.corporatename | College of Sciences | |
| local.contributor.corporatename | School of Mathematics | |
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| relation.isAuthorOfPublication | a38bad34-41fc-48e0-88bc-fc9e3ce89209 | |
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| relation.isOrgUnitOfPublication | 84e5d930-8c17-4e24-96cc-63f5ab63da69 | |
| thesis.degree.level | Doctoral |