Name
Abstract | ||
|---|---|---|
Let the integers 1, . . . ,n be assigned colors. Szemerédi's theorem implies that if there is a dense color class then there is an arithmetic progression of length three in that color. We study the conditions on the color classes forcing totally multicolored arithmetic progressions of length 3.Let f(n) be the smallest integer k such that there is a coloring of {1, . . . ,n} without totally multicolored arithmetic progressions of length three and such that each color appears on at most k integers. We provide an exact value for f(n) when n is sufficiently large, and all extremal colorings. In particular, we show that f(n)=8n/17+O(1). This completely answers a question of Alon, Caro and Tuza. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1007/s00373-006-0663-2 | Graphs and Combinatorics |
Keywords | Field | DocType |
extremal colorings,arithmetic progressions,exact value,smallest integer k,k integer,sub-ramsey,arithmetic progression,color class,sub-ramsey numbers,bounded colorings,multicolored arithmetic progression,dense color class,ramsey number | Integer,Discrete mathematics,Combinatorics,Dirichlet's theorem on arithmetic progressions,Root of unity modulo n,Arithmetic,Ramsey's theorem,Mathematics,Arithmetic progression | Journal |
Volume | Issue | ISSN |
22 | 3 | 1435-5914 |
Citations | PageRank | References |
5 | 0.86 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Maria Axenovich | 1 | 209 | 33.90 |
| Ryan Martin | 2 | 144 | 14.43 |