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arXiv · 1211.2662

Recognizing Interval Bigraphs by Forbidden Patterns

Arash Rafiey
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Abstract

Let H be a connected bipartite graph with n nodes and m edges. We give an O(nm) time algorithm to decide whether H is an interval bigraph. The best known algorithm has time complexity O(nm^6(m + n) \log n) and it was developed in 1997 [18]. Our approach is based on an ordering characterization of interval bigraphs introduced by Hell and Huang [13]. We transform the problem of finding the desired ordering to choosing strong components of a pair-digraph without creating conflicts. We make use of the structure of the pair-digraph as well as decomposition of bigraph H based on the special components of the pair-digraph. This way we make explicit what the difficult cases are and gain efficiency by isolating such situations.

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Arash Rafiey. 2012-11-12. Recognizing Interval Bigraphs by Forbidden Patterns. https://arxiv.org/abs/1211.2662

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