Ore-type conditions for the existence of even image-factors in graphs

For even image, an even image-factor is a spanning subgraph each of whose degree is even between 2 and b. The main result is the following: a 2-edge-connected graph G of order n has an even image-factor if the degree sum of each pair of nonadjacent vertices in G is at least image. These lower bounds are best possible in some sense. The condition “2-edge-connected” cannot be dropped. This result was conjectured by Kouider and Vestergaard, and also is related to the study of Hamilton cycles, connected factors, spanning k-walks, and supereulerian graphs. Moreover, a related open problem is posed.