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Tight toughness, isolated toughness and binding number bounds for (풜, n)-critical deleted graphs.

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Title: Tight toughness, isolated toughness and binding number bounds for (풜, n)-critical deleted graphs.
Authors: Li, Run1 (AUTHOR), Zhang, Shumin1,2 (AUTHOR) zhangshumin@qhnu.edu.cn, Ye, Chengfu1 (AUTHOR)
Source: RAIRO: Operations Research (2804-7303). 2026, Vol. 60 Issue 1, p259-268. 10p.
Subjects: Graph theory, Subgraphs, Graph connectivity
Abstract: For a family 풜 of connected graphs, an 풜-factor is a spanning subgraph of a graph, whose components are isomorphic to a member of 풜. A graph G is called an 풜-factor deleted graph if G – e has an 풜-factor for any e ∈ E(G). A graph G is called an (풜,n)-critical deleted graph if for any Vˊ ⊆ V(G) with |Vˊ| = n, G – Vˊ is an 풜-factor deleted graph. Clearly, an (풜,0)-critical deleted graph is an 풜-factor deleted graph. In this paper, we write 풜 = {K2, C2i+1: i ≥ 2} and give several sufficient conditions for a graph to be an (풜, n)-critical deleted graph. [ABSTRACT FROM AUTHOR]
Copyright of RAIRO: Operations Research (2804-7303) is the property of EDP Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Tight toughness, isolated toughness and binding number bounds for (풜, n)-critical deleted graphs.
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  Data: <searchLink fieldCode="AR" term="%22Li%2C+Run%22">Li, Run</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhang%2C+Shumin%22">Zhang, Shumin</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> zhangshumin@qhnu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Ye%2C+Chengfu%22">Ye, Chengfu</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22RAIRO%3A+Operations+Research+%282804-7303%29%22">RAIRO: Operations Research (2804-7303)</searchLink>. 2026, Vol. 60 Issue 1, p259-268. 10p.
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  Data: <searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Subgraphs%22">Subgraphs</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+connectivity%22">Graph connectivity</searchLink>
– Name: Abstract
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  Data: For a family 풜 of connected graphs, an 풜-factor is a spanning subgraph of a graph, whose components are isomorphic to a member of 풜. A graph G is called an 풜-factor deleted graph if G – e has an 풜-factor for any e ∈ E(G). A graph G is called an (풜,n)-critical deleted graph if for any Vˊ ⊆ V(G) with |Vˊ| = n, G – Vˊ is an 풜-factor deleted graph. Clearly, an (풜,0)-critical deleted graph is an 풜-factor deleted graph. In this paper, we write 풜 = {K2, C2i+1: i ≥ 2} and give several sufficient conditions for a graph to be an (풜, n)-critical deleted graph. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of RAIRO: Operations Research (2804-7303) is the property of EDP Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1051/ro/2025169
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        Text: English
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      – SubjectFull: Graph connectivity
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      – TitleFull: Tight toughness, isolated toughness and binding number bounds for (풜, n)-critical deleted graphs.
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              Text: 2026
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