G if and only if the edge e is not a part of any cycle in g. Cycles c n are 2connected, as are complete graphs k n for n 2. Remove the edge with the highest weight from the cycle. If gis 2connected, then g 2, since if a vertex has degree 1 in a connected graph with more than two vertices, then its neighbor is a cutvertex. Removing a vertex that is not a leaf disconnects the graph, since otherwise there. Pdf edge disjoint spanning trees in an undirected graph. The problem of finding kedgeconnected components is a fundamental problem in computer science. An edge cut is a set of edges of the form s,s for some s. It is easy to see that every 2connected graph is 2edgeconnected, as otherwise any bridge in this graph on.
Given a graph g v, e, the problem is to partition the vertex set v into v1, v2, vh, where. A simple algorithm would, for every pair u,v, determine the maximum flow from u to v with the capacity of all edges in g set to 1 for both directions. It grows this set based on the node closest to source using one. A simple algorithm for finding all k edgeconnected components article pdf available in plos one 109. A connected graph g is called 2connected, if for every vertex. The edgeconnectivity of a connected graph g, written g, is the minimum size of a disconnecting set. A graph g is 2edge connected if and only if it is connected and contains no bridges. A simple test on 2vertex and 2edgeconnectivity arxiv.