Independent dominating sets and hamiltonian cycles

A graph is uniquely hamiltonian if it contains exactly one hamiltonian cycle. In this note we prove that there are no r-regular uniquely hamiltonian graphs when r > 22. This improves upon earlier results of Thomassen. Key words: C-independent set, Lov´asz Local Lemma, Uniquely hamiltonian

• Type: Journal
• Year: 2007
• Where: JGT
• Authors: Penny E. Haxell, Ben Seamone, Jacques Verstraëte
• Keywords: Hamiltonian Cycle, Hamiltonian Graphs, JGT 2007, Lov´asz Local Lemma