Georgia Institute of Technology College of Sciences

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 Four Color Theorem, Hadwiger's conjecture for $K_6$, and Jorgensen'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.

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)