Linkages in Polytope Graphs
Combinatorics
2007-10-22 v1
Abstract
A graph is k-linked if any k disjoint vertex-pairs can be joined by k disjoint paths. We improve a lower bound on the linkedness of polytopes slightly, which results in exact values for the minimal linkedness of 7-, 10- and 13-dimensional polytopes. We analyze in detail linkedness of polytopes on at most (6d+7)/5 vertices. In that case, a sharp lower bound on minimal linkedness is derived, and examples meeting this lower bound are constructed. These examples contain a class of examples due to Gallivan.
Keywords
Cite
@article{arxiv.0710.3726,
title = {Linkages in Polytope Graphs},
author = {Axel Werner and Ronald F. Wotzlaw},
journal= {arXiv preprint arXiv:0710.3726},
year = {2007}
}
Comments
14 pages, 4 figures