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Disjoint paths


Graph Theory » Basic G.T. » Connectivity

Kriesell's Conjecture ★★

Author(s): Kriesell

Conjecture   Let $ G $ be a graph and let $ T\subseteq V(G) $ such that for any pair $ u,v\in T $ there are $ 2k $ edge-disjoint paths from $ u $ to $ v $ in $ G $. Then $ G $ contains $ k $ edge-disjoint trees, each of which contains $ T $.

Keywords: Disjoint paths; edge-connectivity; spanning trees

Posted by Jon Noel
updated August 25th, 2013
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Graph Theory

Approximation Ratio for Maximum Edge Disjoint Paths problem ★★

Author(s): Bentz

Conjecture   Can the approximation ratio $ O(\sqrt{n}) $ be improved for the Maximum Edge Disjoint Paths problem (MaxEDP) in planar graphs or can an inapproximability result stronger than $ \mathcal{APX} $-hardness?

Keywords: approximation algorithms; Disjoint paths; planar graph; polynomial algorithm

Posted by jcmeyer
updated April 18th, 2010
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