A NEW PROOF OF VALIDITY OF BOUCHET'S CONJECTURE ON EULERIAN BIDIRECTED GRAPHS

Recently, E. Macajova and M. Skoviera proved that every bidirected Eulerian graph which admits a nowhere zero ow, admits a nowhere zero 4- ow. This result shows the validity of Bouchet's nowhere zero conjecture for Eulerian bidirected graphs. In this paper we prove the same theorem in a different terminology and with a short and simple proof. More precisely, we prove that every Eulerian undirected graph which admits a zero-sum ow, admits a zero-sum 4- ow. As a conclusion we obtain a shorter proof for the previously mentioned result of Macajova and Skoviera