Degree conditions for group connectivity

AbstractLet G be a 2-edge-connected simple graph on n≥13 vertices and A an (additive) abelian group with |A|≥4. In this paper, we prove that if for every uv∉E(G), max{d(u),d(v)}≥n/4, then either G is A-connected or G can be reduced to one of K2,3,C4 and C5 by repeatedly contracting proper A-connected subgraphs, where Ck is a cycle of length k. We also show that the bound n≥13 is the best possible