论文信息 - Biased graphs whose matroids are special binary matroids

Biased graphs whose matroids are special binary matroids

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), L0(Ω). We determine all biased graphs for which any of these matroids is isomorphic to the Fano plane, the polygon matroid ofK4,K5 orK3,3, any of their duals, Bixby's regular matroidR10, or the polygon matroid ofKm form > 5. In each case the bias is derived from edge signs. We conclude by finding the biased graphsΩ for whichL0(Ω) is not a graphic [or, regular matroid but every proper contraction is.

Thomas Zaslavsky | T. Zaslavsky

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