Matchings in starlike trees

Abstract

Let m(G,k) be the number of k-matchings in the graph G. We write G 1 G 2 if m(G 1 , k) ≤ m(G 2 , k) for all k = 1, 2,.... A tree is said to be starlike if it possesses exactly one vertex of degree greater than two. The relation T 1 T 2 is shown to hold for various pairs of starlike trees T 1 , T 2 . The starlike trees (with a given number of vertices), extremal with respect to the relation , are characterized. © 2001 Elsevier Science Ltd. All rights reserved.