Recognizing Bipartite Tolerance Graphs in Linear Time
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 pre...
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| Published in | Graph-Theoretic Concepts in Computer Science pp. 12 - 20 |
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| Main Authors | , |
| Format | Book Chapter |
| Language | English |
| Published |
Berlin, Heidelberg
Springer Berlin Heidelberg
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| Series | Lecture Notes in Computer Science |
| Online Access | Get full text |
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| Summary: | 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. |
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| ISBN: | 9783540748380 3540748385 |
| ISSN: | 0302-9743 1611-3349 |
| DOI: | 10.1007/978-3-540-74839-7_2 |