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
Zhang, Heping, Dong Ye, and Wai Chee Shiu. "Forcing matching numbers of fullerene graphs." Discrete Applied Mathematics 158.5 (2010): 573-582.