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JCT
2007
133views more  JCT 2007»
13 years 8 months ago
Biased graphs. VII. Contrabalance and antivoltages
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...
Thomas Zaslavsky
JGT
2010
113views more  JGT 2010»
13 years 6 months ago
Crossing numbers of imbalanced graphs
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...
János Pach, József Solymosi, G&aacut...
ACSC
2005
IEEE
14 years 1 months ago
Large k-Separated Matchings of Random Regular Graphs
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)...
Mihalis Beis, William Duckworth, Michele Zito
JGT
2008
107views more  JGT 2008»
13 years 8 months ago
On planar intersection graphs with forbidden subgraphs
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 ...
János Pach, Micha Sharir
JCT
1998
122views more  JCT 1998»
13 years 7 months ago
Counting 1-Factors in Regular Bipartite Graphs
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...
Alexander Schrijver