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On the Power of Isolation in Planar Graphs

Published:01 August 2011Publication History
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Abstract

We study (deterministic) isolation for certain structures in directed and undirected planar graphs. The motivation for undertaking such a study comes from recent positive results on this topic. For example: Bourke et al. [2009] isolate a directed path in planar graphs and subsequently Datta et al. [2010b] isolate a perfect matching in bipartite planar graphs. Our first observation is that sufficiently strong (and plausible) isolations for certain structures in planar graphs would have strong consequences such as: NL ⊆ ⊕L, Bipartite-Matching ∈ NC, and NP ⊆ ⊕P. Our second observation is that although we do not yet have such strong isolations for arbitrary planar graphs, we do have them for bipartite planar graphs, that is, non-bipartiteness is the main bottleneck.

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    • Published in

      cover image ACM Transactions on Computation Theory
      ACM Transactions on Computation Theory  Volume 3, Issue 1
      August 2011
      35 pages
      ISSN:1942-3454
      EISSN:1942-3462
      DOI:10.1145/2003685
      Issue’s Table of Contents

      Copyright © 2011 ACM

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 1 August 2011
      • Accepted: 1 February 2011
      • Revised: 1 January 2011
      • Received: 1 July 2009
      Published in toct Volume 3, Issue 1

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