International Journal of Mathematics and Mathematical Sciences 
Volume 15 (1992), Issue 4, Pages 757-766
doi:10.1155/S016117129200098X

Connections between the matching and chromatic polynomials

E. J. Farrell1 and Earl Glen Whitehead Jr.2

 1Department of Mathematics, The University of the West Indies, St. Augustine, Trinidad and Tobago
2Department of Mathematics & Statistics, University of Pittsburgh, Pittsburgh 15260, PA, USA
Received 8 June 1990; Revised 6 June 1991

Abstract

The main results established are (i) a connection between the matching and chromatic polynomials and (ii) a formula for the matching polynomial of a general complement of a subgraph of a graph. Some deductions on matching and chromatic equivalence and uniqueness are made.