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 کاملRequiring chords in cycles
R. E. Jamison proved that every cycle of length greater than three in a graph has a chord—in other words, the graph is chordal—if and only if every k-cycle is the sum of k − 2 triangles. This result generalizes to having or not having crossing chords and to having strong chords, with similar characterizations of a variety of graph classes that includes chordal bipartite, distance-hereditary, an...
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 کاملThe i-chords of cycles and paths
An i-chord of a cycle or path is an edge whose endpoints are a distance i ≥ 2 apart along the cycle or path. Motivated by many standard graph classes being describable by the existence of chords, we investigate what happens when i-chords are required for specific values of i. Results include the following: A graph is strongly chordal if and only if, for i ∈ {4, 6}, every cycle C with |V (C)| ≥ ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2018
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2017.09.008