Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6423570 | Discrete Mathematics | 2011 | 31 Pages |
Abstract
We determine upper and lower bounds for the number of maximum matchings (i.e., matchings of maximum cardinality) m(T) of a tree T of given order. While the trees that attain the lower bound are easily characterised, the trees with the largest number of maximum matchings show a very subtle structure. We give a complete characterisation of these trees and derive that the number of maximum matchings in a tree of order n is at most O(1.391664n) (the precise constant being an algebraic number of degree 14). As a corollary, we improve on a recent result by Górska and SkupieÅ on the number of maximal matchings (maximal with respect to set inclusion).
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Clemens Heuberger, Stephan Wagner,