Number Of Perfect Matchings Research Articles

Matchings in benzene chains

An explicit recurrence relation is derived for the matching polynomial of the general benzene chain B n . A table is given for chains of length up to 6. Explicit formulae are then obtained for the first five coefficients of the matching polynomial of B n . Finally, results are deduced for the number of perfect matchings and the number of matchings with two nodes.

An exact upper bound to the maximum number of perfect matchings in cubic pseudographs

The present paper shows that the function Φ (n)=2n+1 is an upper bound to the maximum number of distinct perfect matchings in cubic, connected pseudographs with2n vertices. Moreover examples of pseudographs are given which exactly realize such a bound.

Matchings in regular graphs

We consider k-regular graphs with specified edge connectivity and show how some classical theorems and some new results concerning the existence of matchings in such graphs can be proved by using the polyhedral characterization of Edmonds. In addition, we show that lower bounds of Lovász and Plummer on the number of perfect matchings in bicritical graphs can be improved for cubic bicritical graphs.