In the mathematical subject of matroid theory, the bicircular matroid of a graph G is the matroid B(G) whose points are the edges of G and whose independent sets are the edge sets of pseudoforests of G, that is, the edge sets in which each connected component contains at most one cycle.
The bicircular matroid was introduced by Simões-Pereira (1972) and explored further by Matthews (1977) and others. It is a special case of the frame matroid of a biased graph.
In the mathematical subject of matroid theory, the bicircularmatroid of a graph G is the matroid B(G) whose points are the edges of G and whose independent...
coincide with the cycle matroid of G {\displaystyle G} . If no cycle is distinguished, the frame matroid is the bicircularmatroid of G . {\displaystyle...
pseudoforest; this matroid is known as the bicircularmatroid (or bicycle matroid) of G. The smallest dependent sets for this matroid are the minimal connected...
the graphic matroid of a graph, a subset of edges is independent if the corresponding subgraph is a tree or forest. In the bicircularmatroid, a subset...
called contrabalanced. Contrabalanced biased graphs are related to bicircularmatroids. If B consists of the circles of even length, Ω is called antibalanced...
defined: uniform matroids from their two numeric parameters, graphic matroids, bicircularmatroids, and gammoids from graphs, linear matroids from matrices...
doctoral dissertation, The Transversal Presentations and Graphs of BicircularMatroids, was supervised by Richard A. Brualdi. Neudauer has been funded by...
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