Maximum and minimum matchings for series-parallel networks

Series-parallel networks are often used as models for electric circuits. The authors use series-parallel graphs to represent series-parallel networks. Since, there are many different graph representations for a series-parallel networks, they are interested in studying maximum matching in different graph representations of a single network. The number of edges in a maximum matching of G is called the edge independence number of G ad denoted by β(G). For a network N, the maximum matching number, β(N), is defined to be max{β(G[N])} where G[N] is a graph representation for N. The minimum matching number, β*(N), is defined to be min{β(G[N])}. The authors present linear time algorithms to compute β(N) and β*(N) for any series-parallel network N