Graphical Representations of Graphic Frame Matroids.
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| Title: | Graphical Representations of Graphic Frame Matroids. |
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| Authors: | Chen, Rong1 rongchen@fzu.edu.cn, DeVos, Matthew2 mdevos@sfu.ca, Funk, Daryl2 daryl.funk@gmail.com, Pivotto, Irene3 irene.pivotto@uwa.edu.au |
| Source: | Graphs & Combinatorics. Nov2015, Vol. 31 Issue 6, p2075-2086. 12p. |
| Subjects: | Representations of graphs, Frames (Combinatorial analysis), Matroids, Isomorphism (Mathematics), Graph theory, Mathematical analysis |
| Abstract: | A frame matroid $$M$$ is graphic if there is a graph $$G$$ with cycle matroid isomorphic to $$M$$ . In general, if there is one such graph, there will be many. Zaslavsky has shown that frame matroids are precisely those having a representation as a biased graph; this class includes graphic matroids, bicircular matroids, and Dowling geometries. Whitney characterized which graphs have isomorphic cycle matroids, and Matthews characterized which graphs have isomorphic graphic bicircular matroids. In this paper, we give a characterization of which biased graphs give rise to isomorphic graphic frame matroids. [ABSTRACT FROM AUTHOR] |
| Copyright of Graphs & Combinatorics is the property of Springer Nature 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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 110606514 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Graphical Representations of Graphic Frame Matroids. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Chen%2C+Rong%22">Chen, Rong</searchLink><relatesTo>1</relatesTo><i> rongchen@fzu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22DeVos%2C+Matthew%22">DeVos, Matthew</searchLink><relatesTo>2</relatesTo><i> mdevos@sfu.ca</i><br /><searchLink fieldCode="AR" term="%22Funk%2C+Daryl%22">Funk, Daryl</searchLink><relatesTo>2</relatesTo><i> daryl.funk@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Pivotto%2C+Irene%22">Pivotto, Irene</searchLink><relatesTo>3</relatesTo><i> irene.pivotto@uwa.edu.au</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Graphs+%26+Combinatorics%22">Graphs & Combinatorics</searchLink>. Nov2015, Vol. 31 Issue 6, p2075-2086. 12p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Representations+of+graphs%22">Representations of graphs</searchLink><br /><searchLink fieldCode="DE" term="%22Frames+%28Combinatorial+analysis%29%22">Frames (Combinatorial analysis)</searchLink><br /><searchLink fieldCode="DE" term="%22Matroids%22">Matroids</searchLink><br /><searchLink fieldCode="DE" term="%22Isomorphism+%28Mathematics%29%22">Isomorphism (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: A frame matroid $$M$$ is graphic if there is a graph $$G$$ with cycle matroid isomorphic to $$M$$ . In general, if there is one such graph, there will be many. Zaslavsky has shown that frame matroids are precisely those having a representation as a biased graph; this class includes graphic matroids, bicircular matroids, and Dowling geometries. Whitney characterized which graphs have isomorphic cycle matroids, and Matthews characterized which graphs have isomorphic graphic bicircular matroids. In this paper, we give a characterization of which biased graphs give rise to isomorphic graphic frame matroids. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Graphs & Combinatorics is the property of Springer Nature 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: 10.1007/s00373-014-1497-y Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 2075 Subjects: – SubjectFull: Representations of graphs Type: general – SubjectFull: Frames (Combinatorial analysis) Type: general – SubjectFull: Matroids Type: general – SubjectFull: Isomorphism (Mathematics) Type: general – SubjectFull: Graph theory Type: general – SubjectFull: Mathematical analysis Type: general Titles: – TitleFull: Graphical Representations of Graphic Frame Matroids. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Chen, Rong – PersonEntity: Name: NameFull: DeVos, Matthew – PersonEntity: Name: NameFull: Funk, Daryl – PersonEntity: Name: NameFull: Pivotto, Irene IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2015 Type: published Y: 2015 Identifiers: – Type: issn-print Value: 09110119 Numbering: – Type: volume Value: 31 – Type: issue Value: 6 Titles: – TitleFull: Graphs & Combinatorics Type: main |
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