Geodesic
The quantifier semigroup for bipartite graphs
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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.
DOI : 10.37236/610
Classification : 06F05, 05C25, 06A15 
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     author = {Leonard J. Schulman},
     title = {The quantifier semigroup for bipartite graphs},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/610},
     zbl = {1232.06018},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/610/}
}
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Leonard J. Schulman. The quantifier semigroup for bipartite graphs. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/610

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