University of Birmingham > Talks@bham > Combinatorics and Probability Seminar > Tight Ramsey bounds for multiple copies of a graph

## Tight Ramsey bounds for multiple copies of a graphAdd to your list(s) Download to your calendar using vCal - Matija Bucic, Princeton
- Thursday 13 January 2022, 15:00-16:00
- LTA, additional zoom link: https://bham-ac-uk.zoom.us/j/87124623071.
If you have a question about this talk, please contact Johannes Carmesin. The Ramsey number r(G) of a graph G is the smallest integer n such that any 2-colouring of the edges of a clique on n vertices contains a monochromatic copy of G. Determining the Ramsey number of G is a central problem of Ramsey theory with a long history. Despite this there are very few classes of graphs G for which the value of r(G) is known exactly. One such family consists of large vertex disjoint unions of a fixed graph H, we denote such a graph, consisting of n copies of H by nH. This classical result was proved by Burr, Erdős and Spencer in 1975, who showed r(nH)=(2|H|−α(H))n+c, for some c=c(H), provided n is large enough. Since it did not follow from their arguments, Burr, Erdős and Spencer further asked to determine the number of copies we need to take in order to see this long term behaviour and the value of c. More than 30 years ago Burr gave a way of determining c(H), which only applies when the number of copies n is triple exponential in |H|. We obtain an essentially tight answer to this very old problem of Burr, Erdős and Spencer by showing that the long term behaviour occurs already when the number of copies is single exponential. Joint work with B. Sudakov. This talk is part of the Combinatorics and Probability Seminar series. ## This talk is included in these lists:- Combinatorics and Probability Seminar
- LTA, additional zoom link: https://bham-ac-uk.zoom.us/j/87124623071
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