Final doctoral examination and defense of dissertation of Shijie Xie

Thursday, October 24, 2019 - 1:40pm
Skiles 005

Title: 6-connected graphs are two-three linked

Advisor: Dr. Xingxing Yu, School of Mathematics, Georgia Institute of Technology

Committee:
Dr. Robin Thomas, School of Mathematics, Georgia Institute of Technology
Dr. Prasad Tetali, School of Mathematics, Georgia Institute of Technology
Dr. Lutz Warnke, School of Mathematics, Georgia Institute of Technology
Dr. Richard Peng, School of Computer Science, Georgia Institute of Technology

Reader: Dr. Gexin Yu, Department of Mathematics, College of William and Mary

Summary: Let $G$ be a graph and $a_0, a_1, a_2, b_1,$ and $b_2$ be distinct vertices of $G$. Motivated by their work on J\o rgensen's conjecture, Robertson and Seymour asked when does $G$ contain disjoint connected subgraphs $G_1, G_2$, such that $\{a_0, a_1, a_2\}\subseteq V(G_1)$ and $\{b_1, b_2\}\subseteq V(G_2)$. We prove that if $G$ is 6-connected then such $G_1,G_2$ exist. Joint work with Robin Thomas and Xingxing Yu.