Elementary proofs of (relatively) recent characterizations of Eulerian graphs
Abstract Apart from the classical characterization of Eulerian graphs by Eulerian trails and cycle decompositions, there are other characterization theorems due to Toida and McKee, and to Shank respectively. However, while the proof of the Toida-McKee characterization theprem uses, partly, matroid theory, the proof of Shank's characterization theorem is based on considerations of binary vector spaces. In this paper, elementary graph theoretical proofs of these characterization theorems are presented.