Connected [k,k+1]-factors of graphs

Let k be an odd integer greater than or equal to 3, and G be a connected graph of odd order n with n greater than or equal to 4k - 3, and minimum degree at least k. In this paper it is proved that if for each pair of nonadjacent vertices u, v in G max{d(G)(u), d(G)(v)}greater than or equal to n/2, then G has an almost k(+/-)-factor F+/- and a matching M such that F- and M are edge-disjoint and F- + M is a connected [k, k + 1]-factor of G (an almost k(+/-)-factor F+/- is a factor that every vertex has degree k except at most one with degree k +/- 1). As an immediate consequence, the result gives a solution to a problem of Kano on the existence of connected [k, k + 1]-factors.