Department of Mathematics
Forcing matching numbers of fullerene graphs
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. © 2009 Elsevier B.V. All rights reserved.
Degree of freedom, Forcing number, Fullerene graph, Perfect matching
Source Publication Title
Discrete Applied Mathematics
Link to Publisher's Edition
Zhang, H., Ye, D., & Shiu, W. (2010). Forcing matching numbers of fullerene graphs. Discrete Applied Mathematics, 158 (5), 573-582. https://doi.org/10.1016/j.dam.2009.10.013