A class of non-matchable distributive lattices
Abstract
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 -transformation directed graph of the graph. A finite distributive lattice is matchable if its Hasse diagram is isomorphic to a -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.
Cite
@article{arxiv.1810.07332,
title = {A class of non-matchable distributive lattices},
author = {Xu Wang and Xuxu Zhao and Haiyuan Yao},
journal= {arXiv preprint arXiv:1810.07332},
year = {2018}
}
Comments
6 pages, 3 figures