2014/03/30 by Rong Chen, Chen, Rong, Matt DeVos +5 · 1 citation
Computer Science · Engineering · #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1403.7733
openalex publication_date 2014/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.