Title:
NON-SEPARATING PATHS IN GRAPHS
NON-SEPARATING PATHS IN GRAPHS
| dc.contributor.advisor | Yu, Xingxing | |
| dc.contributor.author | Qian, Yingjie | |
| dc.contributor.committeeMember | Bernshteyn, Anton | |
| dc.contributor.committeeMember | Blekherman, Grigoriy | |
| dc.contributor.committeeMember | Song, Zi-Xia | |
| dc.contributor.committeeMember | Wang, Zhiyu | |
| dc.contributor.department | Mathematics | |
| dc.date.accessioned | 2022-08-25T13:37:03Z | |
| dc.date.available | 2022-08-25T13:37:03Z | |
| dc.date.created | 2022-08 | |
| dc.date.issued | 2022-08-01 | |
| dc.date.submitted | August 2022 | |
| dc.date.updated | 2022-08-25T13:37:03Z | |
| dc.description.abstract | When developing a theory for 3-connected graphs, Tutte showed that for any 3-connected graph G and any three vertices a, b, c of G, G-c has an a-b path P such that G-P is connected. We call paths non-separating if their removal results in a graph satisfying a certain connectivity constraint. There is a series of work on non-separating paths in graphs and their applications. For any graph G and distinct vertices a,b,c,d in V(G), we give a structural characterization for G not containing a path A from a to b and avoiding c and d such that removing A from G results in a 2-connected graph. Using this structure theorem, we construct a 7-connected such graph. We will also discuss potential applications to other problems, including the 3-linkage conjecture made by Thomassen in 1980. This is based on joint work with Shijie Xie and Xingxing Yu. | |
| dc.description.degree | Ph.D. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1853/67276 | |
| dc.language.iso | en_US | |
| dc.publisher | Georgia Institute of Technology | |
| dc.subject | non-separting paths | |
| dc.subject | linkage problem | |
| dc.title | NON-SEPARATING 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 |