On 3-edge-connected supereulerian graphs in graph family C(l, k)

Let l > 0 and k ≥ 0 be two integers. Denote by C(l, k) the family of 2-edge-connected graphs such that a graph G ∈ C(l, k) if and only if for every bond S ⊂ E(G) with |S| ≤ 3, each component of G − S has order at least (|V (G)| − k)/l. In this paper we prove that if a 3-edge-connected graph G ∈ C(12, 1), then G is supereulerian if and only if G cannot be contracted to the Petersen graph. Our result extends some results by Chen and by Niu and Xiong. Some applications are also discussed. © 2010 Elsevier B.V. All rights reserved.