Ghareghani, N. (2017). A new proof of validity of Bouchet's conjecture on Eulerian bidirected graphs. Transactions on Combinatorics, 6(2), 31-35. doi: 10.22108/toc.2017.21362

Narges Ghareghani. "A new proof of validity of Bouchet's conjecture on Eulerian bidirected graphs". Transactions on Combinatorics, 6, 2, 2017, 31-35. doi: 10.22108/toc.2017.21362

Ghareghani, N. (2017). 'A new proof of validity of Bouchet's conjecture on Eulerian bidirected graphs', Transactions on Combinatorics, 6(2), pp. 31-35. doi: 10.22108/toc.2017.21362

Ghareghani, N. A new proof of validity of Bouchet's conjecture on Eulerian bidirected graphs. Transactions on Combinatorics, 2017; 6(2): 31-35. doi: 10.22108/toc.2017.21362

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 a nowhere zero $4$-flow. 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 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.