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

Let l0 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.