2018/10/17 by Xu Wang, Wang, Xu, Xuxu Zhao +3
Computer Science · Decision Sciences · #05C70 #06D50 #Advanced Algebra and Logic #Combinatorics (math.CO) #FOS: Mathematics #Fuzzy and Soft Set Theory #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.1810.07332
openalex publication_date 2018/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The set of all perfect matchings of a plane (weakly) elementary bipartite graph equipped with a partial order is a poset, moreover the poset is a finite distributive lattice and its Hasse diagram is isomorphic to Z-transformation directed graph of the graph. A finite distributive lattice is matchable if its Hasse diagram is isomorphic to a Z-transformation directed graph of a plane weakly elementary bipartite graph, otherwise non-matchable. We introduce the meet-irreducible cell with respect to a perfect matching of a plane (weakly) elementary bipartite graph and give its equivalent characterizations. Using these, we extend a result on non-matchable distributive lattices, and obtain a class of new non-matchable distributive lattices.