Abstract
Abiased graph is a graph together with a class of polygons such that no theta subgraph contains exactly two members of the class. To a biased graphΩ are naturally associated three edge matroids:G(Ω), L(Ω), L 0 (Ω). We determine all biased graphs for which any of these matroids is isomorphic to the Fano plane, the polygon matroid ofK 4,K 5 orK 3,3, any of their duals, Bixby's regular matroidR 10, or the polygon matroid ofK m form > 5. In each case the bias is derived from edge signs. We conclude by finding the biased graphsΩ for whichL 0 (Ω) is not a graphic [or, regular matroid but every proper contraction is.
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Research supported by National Science Foundation grant DMS-8407102 and SGPNR grant 85Z0701
Visiting Research Fellow, 1984–1985
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Zaslavsky, T. Biased graphs whose matroids are special binary matroids. Graphs and Combinatorics 6, 77–93 (1990). https://doi.org/10.1007/BF01787483
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DOI: https://doi.org/10.1007/BF01787483