Transversal signed-graphic matroids

Transversal signed-graphic matroids

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Vaidy Sivaraman , Binghamton University
Fine Hall 224

Signed-graphic matroids are a genuine generalization of graphic matroids, and a lot of research has been done on determining to what extent we can transfer properties of graphic matroids to signed-graphic matroids. In this talk we focus on two theorems from the 1970s. The first one, due to Matthews, characterizes graphs whose bicircular matroids are graphic. We characterize graphs whose bicircular matroids are signed-graphic. The second one, due to Bondy and Las Vergnas, characterizes graphs whose cycle matroids are transversal. We attempt to characterize signed graphs whose frame matroids are transversal. Time permitting, we will discuss the issue of basis counting in different classes of matroids, and progress on a related conjecture of Welsh.