Graphical Representations of Graphic Frame Matroids

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

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)


    © 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 languageEnglish
    Pages (from-to)2075-2086
    Number of pages12
    JournalGraphs and Combinatorics
    Issue number6
    Early online date14 Mar 2015
    Publication statusPublished - Nov 2015


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