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Graphical Representations of Graphic Frame Matroids

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 14 Mar 2015Embargo end date: 01 Jan 2014 English Publisher:Springer Science and Business Media LLCJournal:Graphs and Combinatorics, volume 31, pages 2,075-2,086 (issn: 0911-0119, eissn: 1435-5914,

Authors: Matt DeVos; Irene Pivotto; Rong Chen; Daryl Funk;

doi: 10.1007/s00373-014-1497-y , 10.48550/arxiv.1403.7733

arXiv: http://arxiv.org/abs/1403.7733

Graphical Representations of Graphic Frame Matroids

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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 characterised 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.

Related Organizations

University of Western Australia
Australia
Simon Fraser University
Canada
Fuzhou University
China (People's Republic of)
Fuzhou University

Keywords

FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)

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