An additive version of Ramsey's theorem

Details An additive version of Ramsey's theorem An additive version of Ramsey's theorem

2012-02-12

arxiv.org/abs/1202.2582v2

Mathematics

Combinatorics

Scientific paper

We show that, for every $r, k$, there is an $n = n(r,k)$ so that any $r$-coloring of the edges of the complete graph on $[n]$ will yield a monochromatic complete subgraph on vertices ${a + \sum_{i \in I} d_i \mid I \subseteq [k]}$ for some choice of $a, d_1,..., d_k$. In particular, there is always a solution to $x_1 + ... + x_\ell = y_1 + ... + y_\ell$ whose induced subgraph is monochromatic.

Affiliated with

Also associated with

No associations

Rating

An additive version of Ramsey's theorem 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 An additive version of Ramsey's theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An additive version of Ramsey's theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-680465