The size-Ramsey number of trees
Article first published online: 1 APR 2011
Copyright © 2011 Wiley Periodicals, Inc.
Random Structures & Algorithms
Volume 40, Issue 1, pages 49–73, January 2012
How to Cite
Dellamonica, D. (2012), The size-Ramsey number of trees. Random Struct. Alg., 40: 49–73. doi: 10.1002/rsa.20363
- Issue published online: 23 NOV 2011
- Article first published online: 1 APR 2011
- Manuscript Accepted: 15 OCT 2010
- Manuscript Received: 14 APR 2010
- size-Ramsey number;
- expander graphs
Given a graph G, the size-Ramsey number is the minimum number m for which there exists a graph F on m edges such that any two-coloring of the edges of F admits a monochromatic copy of G.
In 1983, J. Beck introduced an invariant β(·) for trees and showed that . Moreover he conjectured that . We settle this conjecture by providing a family of graphs and an embedding scheme for trees. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011