Ore-type conditions implying 2-factors consisting of short cycles

For every graph G , let σ 2 ( G ) = min { d ( x ) + d ( y ) : x y ∉ E ( G ) } . The main result of the paper says that every n -vertex graph G with σ 2 ( G ) ≥ 4 n 3 − 1 contains each spanning subgraph H all whose components are isomorphic to graphs in { K 1 , K 2 , C 3 , K 4 − , C 5 + } . This generalizes the earlier results of Justesen, Enomoto, and Wang, and is a step towards an Ore-type analogue of the Bollobás–Eldridge–Catlin Conjecture.