The computational complexity of graph contractions II: Two tough polynomially solvable cases

  • Authors:

  • Asaf Levin;Daniel Paulusma;Gerhard J. Woeginger

  • Affiliations:

  • Department of Statistics, The Hebrew University, Jerusalem 91905, Israel;Department of Computer Science, Durham University, Science Laboratories, South Road, Durham DH1 3LE, England;Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands

  • Venue:
  • Networks
  • Year:
  • 2008

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Abstract

For a fixed pattern graph H, let H-CONTRACTIBILITY denote the problem of deciding whether a given input graph is contractible to H. This article is part II of our study on the computational complexity of the H-CONTRACTIBILITY problem. In the first article we pinpointed the complexity for all pattern graphs with five vertices except for two pattern graphs H. Here, we present polynomial time algorithms for these two remaining pattern graphs. Interestingly, in all connected cases that are known to be polynomially solvable, the pattern graph H has a dominating vertex, whereas in all cases that are known to be NP-complete, the pattern graph H does not have a dominating vertex. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008