A Note on the 3-Edge-Connected Supereulerian Graphs

For two integers l > 0 and k � 0, define C(l, k) to be the family of 2-edge connected graphs such that a graph G 2 C(l, k) if and only if for every bond SE(G) with |S| � 3, each component of G S has order at least (|V (G)| k)/l. In this note we prove that if a 3- edge-connected simple graph G is in C(10,3), then G is supereulerian if and only if G cannot be contracted to the Petersen graph. Our result extends an earlier result in (Supereulerian graphs and Petersen graph. JCMCC 1991, 9: 79-89) by Chen.