We examine the specialization to simple matroids of certain problems in extremal matroid theory that are concerned with bounded cocircuit size. Assume that each cocircuit of a simp...
We present an algorithm which takes a graph as input and decides in cubic time if the graph is the cocircuit graph of a uniform oriented matroid. In the affirmative case the algor...
Given a 3-connected biased graph with three node-disjoint unbalanced circles, at most one of which is a loop, we describe how the bias matroid of is uniquely represented by .
: A well-known result of Tutte states that a 3-connected graph G is planar if and only if every edge of G is contained in exactly two induced non-separating circuits. Bixby and Cun...