Characterization of 1-tough graphs using factors
نویسندگان
چکیده
منابع مشابه
Chordality and 2-factors in Tough Graphs
A graph G is chordal if it contains no chordless cycle of length at least four and is k-chordal if a longest chordless cycle in G has length at most k. In this note it is proved that all 2 -tough 5-chordal graphs have a 2-factor. This result is best possible in two ways. Examples due to Chvátal show that for all > 0 there exists a ( 2 − )-tough chordal graph with no 2-factor. Furthermore, examp...
متن کاملTwo - tough graphs and f - factors with given properties ∗
Let G be a 2-tough graph on at least five vertices and let e1, e2 be any two edges of G. Katerinis and Wang [6] showed that there exists a 2-factor in G including/excluding e1 and e2. In this paper, we generalize their result by considering the existence of an f -factor including/excluding e1 and e2, where f : V (G) → {1, 2}.
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In this paper we prove that every 1-tough graph has a partition of its vertices into paths of length at least two. ∗This work was partially supported by Projet BQR.
متن کاملForbidden subgraphs for hamiltonicity of 1-tough graphs
A graph G is said to be 1-tough if for every vertex cut S of G, the number of components of G − S does not exceed |S|. Being 1-tough is an obvious necessary condition for a graph to be hamiltonian, but it is not sufficient in general. We study the problem of characterizing all graphs H such that every 1-tough H-free graph is hamiltonian. We almost obtain a complete solution to this problem, lea...
متن کاملHamilton cycles in 1-tough triangle-free graphs
A graph G is called triangle-free if G has no induced K3 as a subgraph. We set 3 = min{3i=1 d(vi)|{v1; v2; v3} is an independent set of vertices in G}. In this paper, we show that if G is a 1-tough and triangle-free graph of order n with n6 3, then G is hamiltonian. c © 2002 Elsevier Science B.V. All rights reserved.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2020
ISSN: 0012-365X
DOI: 10.1016/j.disc.2020.111901