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On linkages in polytope graphs
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Published/Copyright:
June 9, 2011
Abstract
A graph is k-linked if any k disjoint vertex-pairs can be joined by k disjoint paths. We slightly improve a lower bound on the linkedness of polytopes. This results in exact values for the minimal linkedness of 7-, 10- and 13-dimensional polytopes.
We analyze in detail linkedness of d-polytopes on at most (6d + 7)/5 vertices. In that case, a tight 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.
Received: 2009-04-14
Revised: 2009-07-28
Published Online: 2011-06-09
Published in Print: 2011-July
© de Gruyter 2011
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Articles in the same Issue
- Corrigenda to “Reducible Veronese surfaces”
- John functions for o-minimal domains
- Finite semifields with a large nucleus and higher secant varieties to Segre varieties
- On linkages in polytope graphs
- A Torelli theorem for the moduli space of parabolic Higgs bundles
- Average of the mean curvature integral in complex space forms
- Hilbert domains that admit a quasi-isometric embedding into Euclidean space
- Dual polar spaces of arbitrary rank
- Combinatorial differential geometry and ideal Bianchi–Ricci identities
- Fewnomial bounds for completely mixed polynomial systems
- Visible shorelines for unions of islands
- Right-angled buildings with predetermined rational -Betti numbers
