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On Hamilton cycles in certain planar graphs
Author(s) -
Sanders Daniel P.
Publication year - 1996
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/(sici)1097-0118(199601)21:1<43::aid-jgt6>3.0.co;2-m
Subject(s) - mathematics , combinatorics , planar graph , planar , outerplanar graph , 1 planar graph , discrete mathematics , chordal graph , pathwidth , graph , computer science , line graph , computer graphics (images)
Let G be a 2‐connected plane graph with outer cycle X G such that for every minimal vertex cut S of G with | S | ≤ 3, every component of G\S contains a vertex of X G . 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.