Bicircular signed-graphic matroids
Vaidy Sivaraman

TL;DR
This paper characterizes graphs whose bicircular matroids are signed-graphic, expanding understanding beyond the well-studied cycle and bicircular matroids, with implications for graph theory and matroid theory.
Contribution
It provides a new characterization of graphs with signed-graphic bicircular matroids, extending previous work on graphic and bicircular matroids.
Findings
Characterization of graphs with signed-graphic bicircular matroids
Extension of Matthews' theorem to signed-graphic case
Deeper understanding of matroid structures on graphs
Abstract
Several matroids can be defined on the edge set of a graph. Although historically the cycle matroid has been the most studied, in recent times, the bicircular matroid has cropped up in several places. A theorem of Matthews from late 1970s gives a characterization of graphs whose bicircular matroids are graphic. We give a characterization of graphs whose bicircular matroids are signed-graphic.
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