The spanning 3-connectivity of circuit graphs of matroids.
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| Title: | The spanning 3-connectivity of circuit graphs of matroids. |
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| Authors: | Li, Wen1 (AUTHOR) Lwxju1123@163.com, Xiong, Wei1 (AUTHOR) xingheng-1985@163.com, Wang, Xiaoqian1 (AUTHOR) wxq18563352519@sina.com, Lai, Hong-Jian2,3 (AUTHOR) hjlai2015@hotmail.com |
| Source: | Discrete Applied Mathematics. Jul2026, Vol. 388, p108-115. 8p. |
| Subjects: | Matroids, Graph connectivity, Hamiltonian graph theory, Graph theory |
| Abstract: | A graph G is spanning k -connected if for any two vertices u , v ∈ V (G) and for all integers s with 0 ≤ s ≤ k , G has a subgraph H consisting of s -internally disjoint (u , v) -paths such that V (H) = V (G). Thus, if G is spanning 1-connected, it implies that G is Hamilton-connected. The circuit graph of a matroid M is a simple graph G (M) which has vertex set V (G) = C (M) , the collection of all circuits of M , and edge set E (G) = { C C ′ | C , C ′ ∈ C (M) , | C ∩ C ′ | ≠ 0 }. We prove that every circuit graph of a connected matroid containing at least 4 circuits is spanning 3-connected. This result extends a former result on Hamilton-connectedness of circuit graph of matroids in Li and Liu (2008). [ABSTRACT FROM AUTHOR] |
| Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. 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.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193310414 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: The spanning 3-connectivity of circuit graphs of matroids. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Li%2C+Wen%22">Li, Wen</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> Lwxju1123@163.com</i><br /><searchLink fieldCode="AR" term="%22Xiong%2C+Wei%22">Xiong, Wei</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> xingheng-1985@163.com</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Xiaoqian%22">Wang, Xiaoqian</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> wxq18563352519@sina.com</i><br /><searchLink fieldCode="AR" term="%22Lai%2C+Hong-Jian%22">Lai, Hong-Jian</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<i> hjlai2015@hotmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discrete+Applied+Mathematics%22">Discrete Applied Mathematics</searchLink>. Jul2026, Vol. 388, p108-115. 8p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Matroids%22">Matroids</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+connectivity%22">Graph connectivity</searchLink><br /><searchLink fieldCode="DE" term="%22Hamiltonian+graph+theory%22">Hamiltonian graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: A graph G is spanning k -connected if for any two vertices u , v ∈ V (G) and for all integers s with 0 ≤ s ≤ k , G has a subgraph H consisting of s -internally disjoint (u , v) -paths such that V (H) = V (G). Thus, if G is spanning 1-connected, it implies that G is Hamilton-connected. The circuit graph of a matroid M is a simple graph G (M) which has vertex set V (G) = C (M) , the collection of all circuits of M , and edge set E (G) = { C C ′ | C , C ′ ∈ C (M) , | C ∩ C ′ | ≠ 0 }. We prove that every circuit graph of a connected matroid containing at least 4 circuits is spanning 3-connected. This result extends a former result on Hamilton-connectedness of circuit graph of matroids in Li and Liu (2008). [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. 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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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.dam.2026.02.028 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 8 StartPage: 108 Subjects: – SubjectFull: Matroids Type: general – SubjectFull: Graph connectivity Type: general – SubjectFull: Hamiltonian graph theory Type: general – SubjectFull: Graph theory Type: general Titles: – TitleFull: The spanning 3-connectivity of circuit graphs of matroids. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Li, Wen – PersonEntity: Name: NameFull: Xiong, Wei – PersonEntity: Name: NameFull: Wang, Xiaoqian – PersonEntity: Name: NameFull: Lai, Hong-Jian IsPartOfRelationships: – BibEntity: Dates: – D: 31 M: 07 Text: Jul2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0166218X Numbering: – Type: volume Value: 388 Titles: – TitleFull: Discrete Applied Mathematics Type: main |
| ResultId | 1 |
