Finding Fullerene Patches in Polynomial Time

  • Paul Bonsma
  • Felix Breuer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5878)

Abstract

We consider the following question, motivated by the enumeration of fullerenes. A fullerene patch is a 2-connected plane graph G in which inner faces have length 5 or 6, non-boundary vertices have degree 3, and boundary vertices have degree 2 or 3. The degree sequence along the boundary is called the boundary code of G. We show that the question whether a given sequence S is a boundary code of some fullerene patch can be answered in polynomial time when such patches have at most five 5-faces. We conjecture that our algorithm gives the correct answer for any number of 5-faces, and sketch how to extend the algorithm to the problem of counting the number of different patches with a given boundary code.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Paul Bonsma
    • 1
  • Felix Breuer
    • 2
  1. 1.Computer Science DepartmentHumboldt Universität zu BerlinBerlin
  2. 2.Mathematics DepartmentFreie Universität BerlinBerlin

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