A new proof of validity of Bouchet's conjecture on Eulerian bidirected graphs

Document Type: Research Paper


University of Tehran


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.


Main Subjects

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