Circular-arc graphs with clique cover number two
Journal of Combinatorial Theory Series A
Representing digraphs using intervals or circular arcs
Discrete Mathematics
Bi-arc graphs and the complexity of list homomorphisms
Journal of Graph Theory
Interval bigraphs and circular arc graphs
Journal of Graph Theory
Probe Matrix Problems: Totally Balanced Matrices
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Co-TT graphs and a characterization of split co-TT graphs
Discrete Applied Mathematics
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A bipartite graph is chordal bipartite if it does not contain an induced cycle of length at least six. We give three representation characterizations of chordal bipartite graphs. More precisely, we show that a bipartite graph is chordal bipartite if and only if the complement is the intersection graph of a family of pairwise compatible claws in a weighted hypercircle. (A hypercircle is a graph which consists of internally vertex disjoint paths between two distinguished vertices, and a claw in a hypercircle is a connected subgraph containing exactly one of the two distinguished vertices.) We also introduce two classes of bipartite graphs, both containing interval bigraphs and interval containment bigraphs. They are compatible subtree intersection bigraphs and compatible subtree containment bigraphs. We show that these two classes are identical to the class of chordal bipartite graphs.