Doubly lexical orderings of matrices
SIAM Journal on Computing
Three partition refinement algorithms
SIAM Journal on Computing
Doubly lexical ordering of dense 0–1 matrices
Information Processing Letters
Recognizing interval digraphs and interval bigraphs in polynomial time
Discrete Applied Mathematics
Graph classes: a survey
Linear algorithms to recognize interval graphs and test for the consecutive ones property
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
A note on tolerance graph recognition
Discrete Applied Mathematics
Discrete Applied Mathematics
A characterization of triangle-free tolerance graphs
Discrete Applied Mathematics
The PIGs full monty – a floor show of minimal separators
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
A New Intersection Model and Improved Algorithms for Tolerance Graphs
SIAM Journal on Discrete Mathematics
The Recognition of Tolerance and Bounded Tolerance Graphs
SIAM Journal on Computing
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A graph G = (V,E) is a tolerance graph if each vertex v ∈ V can be associated with an interval of the real line Iv and a positive real number tv in such a way that (uv) ∈ E if and only if |Iv ∩ Iu| ≥ min(tv, tu). No algorithm for recognizing tolerance graphs in general is known. In this paper we present an O(n + m) algorithm for recognizing tolerance graphs that are also bipartite, where n and m are the number vertices and edges of the graph, respectively. We also give a new structural characterization of these graphs based on the algorithm.