Hamiltonian cycles in planar triangulations with no separating triangles
作者:
Michael B. Dillencourt,
期刊:
Journal of Graph Theory
(WILEY Available online 1990)
卷期:
Volume 14,
issue 1
页码: 31-49
ISSN:0364-9024
年代: 1990
DOI:10.1002/jgt.3190140105
出版商: Wiley Subscription Services, Inc., A Wiley Company
数据来源: WILEY
摘要:
AbstractA classical theorem of Hassler Whitney asserts that any maximal planar graph with no separating triangles is Hamiltonian. In this paper, we examine the problem of generalizing Whitney's theorem by relaxing the requirement that the triangulation be a maximal planar graph (i.e., that its outer boundary be a triangle) while maintaining the hypothesis that the triangulation have no separating triangles. It is shown that the conclusion of Whitney's theorem still holds if the chords satisfy a certain sparse‐ness condition and that a Hamiltonian cycle through a graph satisfying this condition can be found in linear time. Upper bounds on the shortness coefficient of triangulations without separating triangles are established. Several examples are given to show that the theorems presented here cannot be extended without strong additional hypotheses. In particular, a 1‐tough, non‐Hamiltonian triangulation with no separating triangles is pres
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