Saturation problems with regularity constraints

For a graph F , we say that another G is -saturated, if -free and adding any edge to would create copy of . We study for given integer n whether there exists regular -vertex -saturated graph, it does, what the smallest number edges such graph. mainly focus on case when complete prove example K 3 vertices every large enough also two relaxed versions problem: only require no supergraph should exist or drop condition newly added new