Linkages in Polytope Graphs

Details Linkages in Polytope Graphs Linkages in Polytope Graphs

2007-10-19

arxiv.org/abs/0710.3726v1

Mathematics

Combinatorics

14 pages, 4 figures

Scientific paper

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.

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