Subgraphs with large degrees and girth (Q1066158)

The author has studied properties of graphs of large girth and minimum degree 3 in J. Comb. Theory, Ser. B 35, 129-141 (1983; Zbl 0537.05034). \textit{W. Mader} [Math. Ann. 194, 295-312 (1971; Zbl 0213.508)] showed that a graph of minimum degree 3 and large girth is contractible to a graph of large minimum degree. As a counterpart to this result the author suggests the following conjecture: For each pair of natural numbers r,g there exists f(r,g) such that any graph of minimum degree at least f(r,g) contains a subgraph of minimum degree r and girth at least g. The author also mentions a result of \textit{L. Pyber}, \textit{V. Rödl}, and \textit{E. Szemerédi} [Regular subgraphs in graphs with large average degree (to appear)].