Abstract
AbstractIt was conjectured by Fan that if a graph G = (V,E) has a nowhere‐zero 3‐flow, then G can be covered by two even subgraphs of total size at most |V| + |E| ‐ 3. This conjecture is proved in this paper. It is also proved in this paper that the optimum solution of the Chinese postman problem and the solution of minimum cycle covering problem are equivalent for any graph admitting a nowhere‐zero 4‐flow.
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