• DocumentCode
    1780731
  • Title

    Counting the Number of Perfect Matchings in K5-Free Graphs

  • Author

    Straub, Sebastian ; Thierauf, Thomas ; Wagner, F.

  • Author_Institution
    Theor. Comput. Sci., Ulm Univ., Ulm, Germany
  • fYear
    2014
  • fDate
    11-13 June 2014
  • Firstpage
    66
  • Lastpage
    77
  • Abstract
    Counting the number of perfect matchings in arbitrary graphs is a #P-complete problem. However, for some restricted classes of graphs the problem can be solved efficiently. In the case of planar graphs, and even for K3,3-free graphs, Vazirani showed that it is in NC2. The technique there is to compute a Pfaffian orientation of a graph. In the case of K5-free graphs, this technique will not work because some K5-free graphs do not have a Pfaffian orientation. We circumvent this problem and show that the number of perfect matchings in K5-free graphs can be computed in polynomial time and we describe a circuit construction in TC2.
  • Keywords
    computational complexity; graph theory; pattern matching; #P-complete problem; K5-free graphs; Pfaffian orientation; arbitrary graphs; circuit construction; perfect matching number counting; polynomial time; Computer science; Educational institutions; Heuristic algorithms; Law; Polynomials; Vectors; K_5-free graphs; counting; perfect matchings;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Computational Complexity (CCC), 2014 IEEE 29th Conference on
  • Conference_Location
    Vancouver, BC
  • Type

    conf

  • DOI
    10.1109/CCC.2014.15
  • Filename
    6875476
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1780731