English

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

R2 v1 2026-06-21T09:34:01.730Z