AbstractWe present an algebraic proof of the following result: a set of edges of a multigraphGis contained in some cycle ofGiff the set contains no odd cocycle ofG(“cycle” means here: edge disjoint sum of elementary cycles). As a corollary we obtain the characterization of sub‐Eulerian graphs given by Boesch et al. [The spanning subgraphs of Eulerian grpahs.J. Graph Theory(1) (1977) 7