On Hamilton cycles in certain planar graphs

Abstract

Let G be a 2-connected plane graph with outer cycle XG such that for every minimal vertex cut S of G with |S| ≤ 3, every component of G\S contains a vertex of XG. A sufficient condition for G to be Hamiltonian is presented. This theorem generalizes both Tutte's theorem that every 4-connected planar graph is Hamiltonian, as well as a recent theorem of Dillencourt about NST-triangulations. A linear algorithm to find a Hamilton cycle can be extracted from the proof. One corollary is that a 4-connected planar graph with the vertices of a triangle deleted is Hamiltonian. © 1996 John Wiley & Sons, Inc.