Matchings in regular graphs: minimizing the partition function

Márton Borbényi, Péter Csikvári

For a graph $G$ on $v(G)$ vertices let $m_k(G)$ denote the number of matchings of size $k$, and consider the partition function $M_G(\lambda )={\sum }_{k=0}^n{m}_k(G){\lambda }^k$. In this paper we s…