Ore-type conditions for the existence of even [2, b]-factors in graphs

For even b >= 2, an even [2, b]-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 [2, b]factor if the degree sum of each pair of nonadjacent vertices in G is at least max{4n/(2 + b), 5}. 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. (c) 2005 Elsevier B.V. All rights reserved.