Hamiltonian cycles in planar triangulations with no separating triangles

摘要: A classical theorem of Hassler Whitney asserts that any maximal planar graph with no separating triangles is Hamiltonian. In this paper, we examine the problem generalizing Whitney's by relaxing requirement triangulation be a (i.e., its outer boundary triangle) while maintaining hypothesis have triangles. It shown conclusion still holds if chords satisfy certain sparse-ness condition and Hamiltonian cycle through satisfying can found in linear time. Upper bounds on shortness coefficient triangulations without are established. Several examples given to show theorems presented here cannot extended strong additional hypotheses. particular, 1-tough, non-Hamiltonian presented.