Counting Hexagonal Patches and Independent Sets in Circle Graphs

  • Paul Bonsma
  • Felix Breuer
Conference paper

DOI: 10.1007/978-3-642-12200-2_52

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6034)
Cite this paper as:
Bonsma P., Breuer F. (2010) Counting Hexagonal Patches and Independent Sets in Circle Graphs. In: López-Ortiz A. (eds) LATIN 2010: Theoretical Informatics. LATIN 2010. Lecture Notes in Computer Science, vol 6034. Springer, Berlin, Heidelberg


A hexagonal patch is a plane graph in which inner faces have length 6, inner vertices have degree 3, and boundary vertices have degree 2 or 3. We consider the following counting problem: given a sequence of twos and threes, how many hexagonal patches exist with this degree sequence along the outer face? This problem is motivated by the enumeration of benzenoid hydrocarbons and fullerenes in computational chemistry. We give the first polynomial time algorithm for this problem. We show that it can be reduced to counting maximum independent sets in circle graphs, and give a simple and fast algorithm for this problem.


graph algorithms computational complexity counting problem planar graph circle graph fullerene hexagonal patch fusene polyhex 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Paul Bonsma
    • 1
  • Felix Breuer
    • 2
  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany
  2. 2.Institut für MathematikFreie Universität BerlinBerlinGermany

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