Topological subgraphs in graphs of large girth

It is proved that for every finite graph H of maximum degree n greater than or equal to 3, there is an integer g(H) such that every finite graph of mi nimum degree n and girth at least g(H) contains a subdivision of H. This ha d been conjectured for H=Kn+1 in [8]. We prove also that every finite 2n-co nnected graph of sufficiently large girth is n-linked, and this is best pos sible for all n greater than or equal to 2.