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Planarizing Gadgets for Perfect Matching Do Not Exist

Published:26 July 2016Publication History
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Abstract

To reduce a graph problem to its planar version, a standard technique is to replace crossings in a drawing of the input graph by planarizing gadgets. We show unconditionally that such a reduction is not possible for the perfect matching problem and also extend this to some other problems related to perfect matching. We further show that there is no planarizing gadget for the Hamiltonian cycle problem.

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    • Published in

      cover image ACM Transactions on Computation Theory
      ACM Transactions on Computation Theory  Volume 8, Issue 4
      July 2016
      97 pages
      ISSN:1942-3454
      EISSN:1942-3462
      DOI:10.1145/2956681
      Issue’s Table of Contents

      Copyright © 2016 ACM

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 26 July 2016
      • Accepted: 1 January 2016
      • Revised: 1 December 2015
      • Received: 1 July 2014
      Published in toct Volume 8, Issue 4

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