On intersections of interval graphs |
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Authors: | HS Witsenhausen |
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Institution: | Bell Laboratories, Murray Hill, NJ 07974, USA |
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Abstract: | If one can associate with each vertex of a graph an interval of a line, so that two intervals intersect just when the corresponding vertices are joined by an edge, then one speaks of an interval graph.It is shown that any graph on v vertices is the intersection (“product”) of at most v] interval graphs on the same vertex set.For v=2k, k factors are necessary for, and only for, the complete k-partite graph K2,2,…,2.Some results for the hypergraph generalization of this question are also obtained. |
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