On vertex-transitive graphs with a unique hamiltonian circle

Speaker: Dave Morris

Date: Mon, Oct 24, 2022

Location: PIMS, University of Lethbridge

Conference: Lethbridge Number Theory and Combinatorics Seminar

Subject: Mathematics, Combinatorics, Number Theory

Class: Scientific


We will discuss graphs that have a unique hamiltonian cycle and are vertex-transitive, which means there is an automorphism that takes any vertex to any other vertex. Cycles are the only examples with finitely many vertices, but the situation is more interesting for infinite graphs. (Infinite graphs do not have "hamiltonian cycles," but there are natural analogues.) The case where the graph has only finitely many ends is not difficult, but we do not know whether there are examples with infinitely many ends. This is joint work in progress with Bobby Miraftab.