AbstractLetGbe a graph of ordernand defineNC(G)= min{|N(u) ∪N(v)| |uv∉E(G)}. A cycleCofGis called adominating cycleorD‐cycleifV(G) ‐V(C) is an independent set. AD‐pathis defined analogously. The following result is proved: ifGis 2‐connected and contains aD‐cycle, thenGcontains aD‐cycle of length at least min{n, 2NC(G)} unlessGis the Petersen graph. By combining this result with a known sufficient condition for the existence of aD‐cycle, a common generalization of Ore's Theorem and several recent “neighborhood union results” is obtained. An analogous result on longD‐pa