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).