Some Exact Ramsey-Turán Numbers

Details Some Exact Ramsey-Turán Numbers Some Exact Ramsey-Turán Numbers

2011-09-21

arxiv.org/abs/1109.4472v2

Mathematics

Combinatorics

11 pages

Scientific paper

Let r be an integer, f(n) a function, and H a graph. Introduced by Erd\H{o}s, Hajnal, S\'{o}s, and Szemer\'edi, the r-Ramsey-Tur\'{a}n number of H, RT_r(n, H, f(n)), is defined to be the maximum number of edges in an n-vertex, H-free graph G with \alpha_r(G) <= f(n) where \alpha_r(G) denotes the K_r-independence number of G. In this note, using isoperimetric properties of the high dimensional unit sphere, we construct graphs providing lower bounds for RT_r(n,K_{r+s},o(n)) for every 2 <= s <= r. These constructions are sharp for an infinite family of pairs of r and s. The only previous sharp construction was by Bollob\'as and Erd\Hos for r = s = 2.

Affiliated with

Also associated with

No associations

Rating

Some Exact Ramsey-Turán 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 Some Exact Ramsey-Turán Numbers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some Exact Ramsey-Turán Numbers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-256971