Spanning Eulerian Subgraphs of 2-Edge-Connected Graphs

Abstract

For integers l and k with l > 0 and k > 0, let ${{\fancyscript{C}}(l, k)}$ denote the family of 2-edge-connected graphs G such that for each bond cut |S| ≤ 3, each component of G − S has at least (|V(G)| − k)/l vertices. In this paper we prove that if ${G\in {\fancyscript{C}}(7, 0)}$ , then G is not supereulerian if and only if G can be contracted to one of the nine specified graphs. Our result extends some earlier results (Catlin and Li in J Adv Math 160:65–69, 1999; Broersma and Xiong in Discrete Appl Math 120:35–43, 2002; Li et al. in Discrete Appl Math 145:422–428, 2005; Li et al. in Discrete Math 309:2937–2942, 2009; Lai and Liang in Discrete Appl Math 159:467–477, 2011).