Elementary Bipartite Graph Research Articles

An extension of elementary bipartite graphs to matroid pairs and its characterization

In this paper we shall present a generalization of elementary bipartite graphs to a certain pair of matroids, which we shall call an “elementary pair”, and show that a matroid pair is elementary if and only if it is irreducible with respect to a decomposition method associated with matroid intersection problems.

On n-extendable graphs

A graph G is said to be n-extendable if it is connected, has a set of n independent lines and every set of n independent lines in G extends to (i.e. is a subset of) a perfect matching of G. Nearly all n-extendable graphs ( n⩾2) are shown to be ( n–1)-extendable and ( n + 1)- connected. The special cases of 2- and 3-extendable graphs and their relationships with bicritical and elementary bipartite graphs are then studied.