Abstract. We develop linear representation theory for bicircular matroids, a chief example being a matroid associated with forests of a graph, and bicircular lift matroids, a chief...
The crossing number, cr(G), of a graph G is the least number of crossing points in any drawing of G in the plane. According to the Crossing Lemma of Ajtai, Chv´atal, Newborn, Sze...
A k-separated matching in a graph is a set of edges at distance at least k from one another (hence, for instance, a 1-separated matching is just a matching in the classical sense)...
Let C be a family of n compact connected sets in the plane, whose intersection graph G(C) has no complete bipartite subgraph with k vertices in each of its classes. Then G(C) has ...
We show that any k-regular bipartite graph with 2n vertices has at least ((k−1)k−1 kk−2 )n perfect matchings (1-factors). Equivalently, this is a lower bound on the permanent...