Partial cubes with pre-hull number at most 1
Combinatorics
2019-01-23 v1
Abstract
We prove that a connected bipartite graph G is a partial cube if and only if the set of attaching points of any copoint of G is convex. A consequence of this result is that any connected bipartite graph with pre-hull number at most 1 is a partial cube. We show that the class of partial cubes with pre-hull number at most 1 is closed under gated subgraphs, gated amalgams and cartesian products.
Keywords
Cite
@article{arxiv.1901.06571,
title = {Partial cubes with pre-hull number at most 1},
author = {Norbert Polat},
journal= {arXiv preprint arXiv:1901.06571},
year = {2019}
}
Comments
15 pages, 1 figure