On bipartite powers of bigraphs

Permutation bigraphs and interval containments

A bipartite graph with partite sets X and Y is a permutation bigraph if there are two linear orderings of its vertices so that xy is an edge for x ∈ X and y ∈ Y if and only if x appears later than y in the first ordering and earlier than y in the second ordering. We characterize permutation bigraphs in terms of representations using intervals. We determine which permutation bigraphs are interva...

Quasimonotone graphs

For any class C of bipartite graphs, we define quasi-C to be the class of all graphs G such that every bipartition of G belongs to C. This definition is motivated by a generalisation of the switch Markov chain on perfect matchings from bipartite graphs to nonbipartite graphs. The monotone graphs, also known as bipartite permutation graphs and proper interval bigraphs, are such a class of bipart...

On Satisfiability Problems with a Linear Structure

It was recently shown [19] that satisfiability is polynomially solvable when the incidence graph is an interval bipartite graph (an interval graph turned into a bipartite graph by omitting all edges within each partite set). Here we relax this condition in several directions: First, we show an FPT algorithm parameterized by k for k-interval bigraphs, bipartite graphs which can be converted to i...

Bipartite probe interval graphs, circular arc graphs, and interval point bigraphs

Relationships between the class of unit grid intersection graphs and other classes of bipartite graphs

We show that the class of unit grid intersection graphs properly includes both of the classes of interval bigraphs and of P6-free chordal bipartite graphs. We also demonstrate that the classes of unit grid intersection graphs and of chordal bipartite graphs are incomparable. © 2007 Elsevier B.V. All rights reserved.