a new proof of validity of bouchet's conjecture on eulerian bidirected graphs

Recently, e. m'{a}v{c}ajov'{a} and m. v{s}koviera proved that every bidirected eulerian graph which admits a nowhere zero flow, admits anowhere zero 4-flow. this result shows the validity of bouchet's nowhere zero conjecture foreulerian 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 flow, admits a zero-sum 4-flow. as a conclusion we obtain a shorter proof for the previously mentioned result of m'{a}v{c}ajov'{a} and v{s}koviera.