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Background: the Ramsey number \$R(r,s)\$ gives the minimum number of vertices \$v\$ in the complete graph \$K_v\$ such that a red/blue edge coloring of \$K_v\$ has at least one red \$K_r\$ or one blue \$K_s\$. Bounds for larger \$r, s\$ are very difficult to establish.
Your task is to output the number \$R(r,s)\$ for \$1 \le r,s \le 5\$.
Input
Two integers \$r, s\$ with \$1 \le r \le 5\$ and \$1 \le s \le 5 \$.
Output
\$R(r,s)\$ as given in this table:
s 1 2 3 4 5
r +--------------------------
1 | 1 1 1 1 1
2 | 1 2 3 4 5
3 | 1 3 6 9 14
4 | 1 4 9 18 25
5 | 1 5 14 25 43-48
Note that \$r\$ and \$s\$ are interchangeable: \$R(r,s) = R(s,r)\$.
For \$R(5,5)\$ you may output any integer between \$43\$ and \$48\$, inclusive. At the time of this question being posted these are the best known bounds.
I think (even with the range for
5,5
) that this may fit under [tag:kolmogorov-complexity] (or does only a non-input, fixed output fit?) – Jonathan Allan – 2018-07-15T19:47:56.947When was 49 excluded for R(5,5)? (I'm not challenging; I seem to have missed a paper after Exoo's and McKay and Radziszowski's.) – Eric Towers – 2018-07-15T21:47:33.743
1
@EricTowers https://arxiv.org/abs/1703.08768
– qwr – 2018-07-15T23:50:37.077@qwr : Thanks! I'm enjoying it so far. – Eric Towers – 2018-07-16T01:42:57.413