Forcing matching numbers of fullerene graphs

Heping Zhang, Dong Ye, Wai Chee SHIU*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

40 Citations (Scopus)


The forcing number or the degree of freedom of a perfect matching M of a graph G is the cardinality of the smallest subset of M that is contained in no other perfect matchings of G. In this paper we show that the forcing numbers of perfect matchings in a fullerene graph are not less than 3 by applying the 2-extendability and cyclic edge-connectivity 5 of fullerene graphs obtained recently, and Kotzig's classical result about unique perfect matching as well. This lower bound can be achieved by infinitely many fullerene graphs.

Original languageEnglish
Pages (from-to)573-582
Number of pages10
JournalDiscrete Applied Mathematics
Issue number5
Publication statusPublished - 6 Mar 2010

Scopus Subject Areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

User-Defined Keywords

  • Degree of freedom
  • Forcing number
  • Fullerene graph
  • Perfect matching


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