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Published May 30, 2011 | Published
Journal Article Open

The quantifier semigroup for bipartite graphs


In a bipartite graph there are two widely encountered monotone mappings from subsets of one side of the graph to subsets of the other side: one corresponds to the quantifier "there exists a neighbor in the subset" and the other to the quantifier "all neighbors are in the subset." These mappings generate a partially ordered semigroup which we characterize in terms of "run-unimodal" words.

Additional Information

© 2011 The Author(s). Submitted: Jun 22, 2010; Accepted: May 17, 2011; Published: May 30, 2011. Supported in part by NSF CCR-0326554, NSF CCF-0515342, NSA H98230-06-1-0074, and NSF CCF-0829909. Thanks to an anonymous referee for helpful comments on the paper.

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