Caleb Fong, Rutgers University

Abstract

Understanding the random graph threshold for "containing H as a subgraph" is not hard when H is a fixed graph. In contrast, when H is a spanning subgraph, the question rapidly becomes more interesting (and difficult!). Some standard examples include H = Hamilton cycle, or H = perfect matching. In this talk, we will consider the case H = T_n (a spanning tree on n vertices) and survey some of the existing work on the problem.