Sharp threshold for the appearance of certain spanning trees in random graphs



We prove that a given tree T on n vertices with bounded maximum degree is contained asymptotically almost surely in the binomial random graph equation image provided that T belongs to one of the following two classes: (1) T has linearly many leaves; (2) T has a path of linear length all of whose vertices have degree two in T. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012