Graphical Representations of Graphic Frame Matroids

R. Chen; M. Devos; D. Funk; Irene Pivotto

doi:10.1007/s00373-014-1497-y

Graphical Representations of Graphic Frame Matroids

R. Chen, M. Devos, D. Funk, Irene Pivotto

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

© 2015, Springer Japan. 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.

Original language	English
Pages (from-to)	2075-2086
Number of pages	12
Journal	Graphs and Combinatorics
Volume	31
Issue number	6
Early online date	14 Mar 2015
DOIs	https://doi.org/10.1007/s00373-014-1497-y
Publication status	Published - Nov 2015

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author = "R. Chen and M. Devos and D. Funk and Irene Pivotto",

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AB - © 2015, Springer Japan. 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.

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DO - 10.1007/s00373-014-1497-y

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JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

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ER -

Graphical Representations of Graphic Frame Matroids

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