منابع مشابه
Chords of Longest Cycles in Cubic Graphs
We describe a general sufficient condition for a Hamiltonian graph to contain another Hamiltonian cycle. We apply it to prove that every longest cycle in a 3-connected cubic graph has a chord. We also verify special cases of an old conjecture of Sheehan on Hamiltonian cycles in 4-regular graphs and a recent conjecture on a second Hamiltonian cycle by Triesch, Nolles, and Vygen. 1997 Academic Press
متن کاملChords of longest circuits in locally planar graphs
It was conjectured by Thomassen ([B. Alspach, C. Godsil, Cycle in graphs, Ann. Discrete Math. 27 (1985)], p. 466) that every longest circuit of a 3-connected graph must have a chord. This conjecture is verified for locally 4-connected planar graphs, that is, let N be the set of natural numbers; then there is a function h : N → N such that, for every 4-connected graph G embedded in a surface S w...
متن کاملChords of longest circuits in 3-connected graphs
Thomassen conjectured that every longest circuit of a 3-connected graph has a chord. The conjecture is veri2ed in this paper for projective planar graphs with minimum degree at least 4. c © 2002 Elsevier Science B.V. All rights reserved.
متن کاملIntersections of longest cycles in grid graphs
Abstract: It is well-known that the largest cycles of a graph may have empty intersection. This is the case, for example, for any hypohamiltonian graph. In the literature, several important classes of graphs have been shown to contain examples with the above property. This paper investigates a (nontrivial) class of graphs which, on the contrary, admits no such example. c © 1997 John Wiley & Son...
متن کاملHamilton Cycles in Cubic Graphs
A graph is cubic if each of its vertex is of degree 3 and it is hamiltonian if it contains a cycle passing through all its vertices. It is known that if a cubic graph is hamiltonian, then it has at least three Hamilton cycles. This paper is about those works done concerning the number of Hamilton cycles in cubic graphs and related problems.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1997
ISSN: 0095-8956
DOI: 10.1006/jctb.1997.1776