A conjecture of Erdős on graph Ramsey numbers

Details A conjecture of Erdős on graph Ramsey numbers A conjecture of Erdős on graph Ramsey numbers

2010-01-30

arxiv.org/abs/1002.0095v1

Mathematics

Combinatorics

Scientific paper

The Ramsey number $r(G)$ of a graph $G$ is the minimum $N$ such that every red-blue coloring of the edges of the complete graph on $N$ vertices contains a monochromatic copy of $G$. Determining or estimating these numbers is one of the central problems in combinatorics. One of the oldest results in Ramsey Theory, proved by Erd\H{o}s and Szekeres in 1935, asserts that the Ramsey number of the complete graph with $m$ edges is at most $2^{O(\sqrt{m})}$. Motivated by this estimate Erd\H{o}s conjectured, more than a quarter century ago, that there is an absolute constant $c$ such that $r(G) \leq 2^{c\sqrt{m}}$ for any graph $G$ with $m$ edges and no isolated vertices. In this short note we prove this conjecture.

Affiliated with

Also associated with

No associations

Rating

A conjecture of Erdős on graph Ramsey numbers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A conjecture of Erdős on graph Ramsey numbers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A conjecture of Erdős on graph Ramsey numbers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-346892