Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, October 04, 2007, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Penny Haxell (Univ. of Waterloo)

Independent dominating sets and Hamilton cycles

A graph is said to be uniquely Hamiltonian if it contains exactly one Hamilton cycle. An old conjecture of Sheehan states that there are no 4-regular uniquely Hamiltonian graphs. We show that there are no r-regular uniquely Hamiltonian graphs for any r>22. We use the approach of Thomassen, who proved that for any graph G with a Hamilton cycle C, if G contains a vertex subset S that is independent in C and dominating in G-C, then G has a Hamilton cycle different from C.

Joint work with B. Seamone and J. Verstraete.

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