Enumeration of Minimal Extensions and Maximal Reduc- tions of Interval Order Sample Clauses

Enumeration of Minimal Extensions and Maximal Reduc- tions of Interval Order. In the same way, enumerating all the maximal chain subgraphs of a bipartite graph G(H) (i.e. our first problem) is equivalent to list all the maximal interval order reductions of the bipartite order H and enumerating all maximal chain subgraphs of B(H) is equivalent to list all minimal interval order extensions of the bipartite order H as minimal interval order extensions of bipartite posets are still bipartite posets (substantially a proof of this is present in the proof of Lemma 4 in [91]). We can then interpret the results on the enumeration of maximal chain subgraphs (Proposition 4 and Proposition 5) in this context as follows:
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