A Note on Sub‐Eulerian Graphs

Abstract

Abstract We present an algebraic proof of the following result: a set of edges of a multigraph G is contained in some cycle of G iff the set contains no odd cocycle of G (“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) 79–84].