  We establish new lower bounds for the convergence radius of the Mayer series
and the Virial series of a continuous particle system interacting via a stable
and tempered pair potential. Our bounds considerably improve those given by
Penrose and Ruelle in 1963 for the Mayer series and by Lebowitz and Penrose in
1964 for the Virial series. To get our results we exploit the tree-graph
identity given by Penrose in 1967 using a new partition scheme based on minumum
spanning trees.
