As is well known, the cycles of any given graph G may be regarded as the circuits of a matroid defined on the edge set of G. The question of whether other ...

We give a simple proof of Tutte's theorem stating that the cycle space of a 3--connected graph is generated by the set of non-separating circuits of the graph.

As is well known, the cycles of any given graph G may be regarded as the circuits of a matroid defined on the edge set of G. The question of whether other ...

A family C of subsets of a set E is a family of circuits of a matroid if and only if C satisfies the properties (C1), (C2) and (C3). We now introduce a notion ...

The basis graph of a matroid has a vertex for each basis and an edge for each pair of bases that differ by the exchange of a single pair of elements.

A base of a matroid M is any inclusion maximal independent set in M, a circuit of a matroid M is any inclusion minimal dependent set in M. Examples. 1. Matric ...

In general, a matroid consists of a finite set E, called the ground set, and a collection C of non-empty incomparable subsets of E, called circuits, that obey ...

In the mathematical theory of matroids, a graphic matroid is a matroid whose independent sets are the forests in a given finite undirected graph.

Results in graphs and line graphs. For a connected graph G not isomorphic to a path, a cycle or a K1,3, let pc(G) denote the.

We can now characterize independent sets, bases and circuits of a matroid obtained by contracting of a subset of its ground set. Proposition 2.9. Let M be a ...