Mateja Šajna (University of Ottawa)
On Sheehan‘s Conjecture for graphs with symmetry

It is known that every (simple) regular graph of degree d that has a Hamilton cycle in fact possesses a second Hamilton cycle if d is odd or d is at least 23. Sheehan conjectured that the statement is also true for d=4, which would imply that it is true for every d greater than 2. Fleischner showed that Sheehan's conjecture fails for 4-regular multigraphs, but it is not difficult to prove it for 4-regular vertex-transitive simple graphs. In this talk, we outline the proof of Sheehan's conjecture for 4-regular simple graphs satisfying certain conditions on the automorphism group that are weaker than vertex transitivity. This is joint work with Andrew Wagner.

Note: This is a half-hour talk. The rest of the hour will be devoted to informal discussion.