Embedding Spanning Trees in Random Graphs

We prove that if T is a tree on n vertices with maximum degree and the edge probability p(n) satisfies: np C max{ log n, n } for some constant > 0, then with high probability the random graph G(n, p) contains a copy of T. The obtained bound on the edge probability is shown to be essentially tight for = n(1) .

• Type: Journal
• Year: 2010
• Where: SIAMDM
• Authors: Michael Krivelevich
• Keywords: Edge Probability, Maximum Degree, Random Graph, SIAMDM 2010