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Forcing matching numbers of fullerene graphs |
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| Authors: | Heping Zhang Wai Chee Shiu |
| Affiliation: | a School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China b Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA c Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong, China |
| Abstract: | 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. |
| Keywords: | Fullerene graph Perfect matching Forcing number Degree of freedom |
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