Toughness and Hamiltonicity of a class of planar graphs Original Research Article

A graph G is called chordal if every cycle of G of length at least four has a chord. By a theorem of Böhme, Harant and Tkáč more than 1-tough chordal planar graphs are Hamiltonian. We prove that this is even true for more than 1-tough planar graphs under the weaker assumption that separating cycles of length at least four have chords.