Listed on this page are current research projects being offered for the Vacation Scholarship Program.
For more information on this research group see: Discrete Mathematics
Hamiltonicity of vertex-transitive graphs
A question of Lovasz in 1969 asked whether every connected Cayley graph with more than two vertices have a Hamilton cycle. This question is still wide open, even for Cayley graphs on some fairly simple families of groups. More surprisingly, there are only a few examples of vertex-transitive graphs known to have no Hamilton cycle, which leads to the conjecture that there are only finitely many vertex-transitive graphs with no Hamilton cycles. The aim of this project is to investigate the Hamiltonicity for some special families of vertex-transitive graphs, especially Cayley graphs.
Contact: Binzhou Xia firstname.lastname@example.org