The structure of minimally t-tough, 2K2-free graphs

A graph G is minimally t-tough if the toughness of G is t and deletion of any edge from G decreases its toughness. Kriesell conjectured that the minimum degree of a minimally 1-tough graph is 2, and Katona et al. proposed a generalized version of the conjecture that the minimum degree of a minimally...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 346; pp. 1 - 9
Main Authors Ma, Hui, Hu, Xiaomin, Yang, Weihua
Format Journal Article
LanguageEnglish
Published Elsevier B.V 31.03.2024
Subjects
[formula omitted]-free graphs
Minimally [formula omitted]-tough graphs
Minimum degree
Toughness
Toughness
2K2-free graphs
Minimum degree
Minimally 1/a-tough graphs
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Summary:A graph G is minimally t-tough if the toughness of G is t and deletion of any edge from G decreases its toughness. Kriesell conjectured that the minimum degree of a minimally 1-tough graph is 2, and Katona et al. proposed a generalized version of the conjecture that the minimum degree of a minimally t-tough graph is ⌈2t⌉. In this paper, we characterize the minimally 1/a-tough, 2K2-free graphs for an integer a.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2023.11.034