文摘
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 160:65-9, 1999; Broersma and Xiong in Discrete Appl Math 120:35-3, 2002; Li et?al. in Discrete Appl Math 145:422-28, 2005; Li et?al. in Discrete Math 309:2937-942, 2009; Lai and Liang in Discrete Appl Math 159:467-77, 2011).