Bicircular signed-graphic matroids

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.