Embedding spanning trees in random graphs

2010/07/14 by Krivelevich, Michael · 4 citations
#05C80 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1007.2326

Abstract

We prove that if T is a tree on n vertices wih maximum degree D and the edge probability p(n) satisfies: np>c*maxD*logn,n^ε for some constant ε>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 D=n^Θ(1).

Cited by

• Asymmetric Ramsey numbers of trees
• Spanning trees with large maximum degrees
• On the Graham--Sloane harmonious labelling conjecture
• Unbounded degree spanning hypertrees in Dirac hypergraphs

Related

• Embedding bounded degree spanning trees in random graphs
• Spanning trees in random graphs
• Spanning trees in randomly perturbed graphs
• Bounded-degree spanning trees in randomly perturbed graphs
• Universality of random graphs and rainbow embedding