On Burgess's theorem and related problems

Let G be a graph. We determine all graphs which are G-like. We also prove t hat if G(i) (i = 1, 2,...,m) are graphs, then in order that each G(i)-like (i = 1, 2,...,m) continuum M be n-indecomposable for some n = n(M) it is ne cessary and sufficient that if K is a graph, then K is not G(i)-like for so me integer i with 1 less than or equal to i less than or equal to m. This g eneralizes a well known theorem of Burgess.