Characterization of Cycle Stochastic Graphs

A simple graph G is said to be a Cycle-Stochastic (CS) graph, if there is a non-negative real-valued function p on the edge set of G such tht for every cycle C of G, p(C) := Σp(e) is equal to 1, where the sum is taken over all the edges e of C. In this paper we characterise the finite cycle stochastic graphs by means of 5 minor forbidden subgraphs. It is also shown that a finite graph G is a cycle stochastic graph if and only if G has no subgraph contractible to K4, the complete graph on 4 vertices or the unique graph on 6 vertices with degree sequence (4,4,4, 2, 2, 2).