Edge Partitions in Undirected Graphs

Abstract

Partitions of the set of edges of an undirected graph are investigated in general. The set of vertices of attachment of a partition and the partition of the W-components of a set of vertices are defined. Their properties show a high degree of duality. An algorithm to find the W-components is presented. The results are applied to a proof of Menger's theorem combined with an algorithm for finding maximal sets of vertex-disjoint paths as well as minimal sets of separating vertices