I decided to [cross-post](https://math.stackexchange.com/questions/70619/submatrix-with-only-0-or-1-entries) the question here from math.stackexchange.com because I got no answer from there.


It is a quick question on bipartite Ramsey numbers (I'm not an expert on the subject, so perhaps the question is trivial).


What is the least positive integer $r$ such that, any $r \times r$ 0-1 matrix contains at least one $3 \times 3$ submatrix filled with only 0 or only 1 entries ?


I found some articles with upper/lower bounds, but not a clear chart with the particular values I need.



3x3 submatrix with only $0$ or $1$ entries
According to this:
MR1622032 (99c:05139) 
Hattingh, Johannes H.(SA-RAND); Henning, Michael A.(SA-NTL2)
Bipartite Ramsey theory. (English summary) 
Util. Math. 53 (1998), 217–230. 
the answer is $17$, not $15.$


**Addition** A proof is contained in Irving's paper "A bipartite Ramsey problem and the Zarankiewicz numbers" (available on line). In the later paper with an almost identical title:


Bipartite Ramsey Numbers and Zarankiewicz Numbers (by Goddard et al) they seem to indicate that the Irving paper is slightly buggy, but that the result holds anyhow.


