On a conjecture about trees in graphs with large girth

The girth of a graph G is the length of a shortest cycle in G. Dobson (1994. Ph.D. dissertation, Louisiana State University, Baton Rouge, LA) conjectured that every graph G with girth at least 2t + 1 and minimum degree at least k/t contains every tree T with k edges whose maximum degree does not exceed the minimum degree of G. The conjecture has been proved for t less than or equal to3. In this paper, we prove Dobson's conjecture. (C) 2001 Academic Press.