Want to see for yourself that R(r,s) actually equals N? Look no further than this program!
This program allows you to see every* nonisomorphic graph on N vertices and how it either contains a K_r or its complement contains a K_s.
g++,sqlite3, geng, and boost.
sqlite3 and fastapi
g++ -std=c++17 -O2 -o gen-rMN gen-rMN.cc -lsqlite3
Ensure sqlite3 is on your include path!
Generate graphs with python geng-util.py.
Make ramsey data with python make-data.py.
Serve HTML fastapi dev server.py.
Navigate to http://localhost:8000/index.html.
Usage: ./gen-rMN r s
r: size of red clique to search for (e.g., 3)
s: size of blue clique to search for (e.g., 4)
Reads graph6 graphs from stdin and writes results to ramsey_results.db.
-h: show this help message
As seen in A000088 the number of nonisomorphic graphs grows rapidly! Thus, it is unrealistic to generate data for all 29 quadrillion graphs on 14 vertices. The script geng-util.sh generates a subset of these graphs which can then be read by the program for a representative sample.
More numbers and statistics to be added shortly!