Appendix for:
J. Dybizbański, A lower bound on the hypergraph Ramsey
number R(4, 5; 3), Contributions to Discrete Mathematics 13(2) (2018) 112-115
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a) simplifed formula:
formula.cnf
Description of cnf file format: http://people.sc.fsu.edu/~jburkardt/data/cnf/cnf.html - b) satisfying assigment: result.txt
- c) R(4,5;3) ≥ 35, corresponding colouring of all triples: colouring.txt (lower bound has been improved from 33 to 35)
- d) program in C++ that verify that the colouring is proper: verif.cpp
Addendum
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Using the same method (edge {a,b,c} has the same colour as edge {a+d, b+d, c+d}, for every d, addition is modulo number of vertices) we found colouring for numbers:
- R(5,5;3) ≥ 88 (previous lower bound 82)
- R(4,6;3) ≥ 63 (previous lower bound 58)
- R(4,4,4;3) ≥ 79 (previous lower bound 56)
- Note that we don't have any negative results i.e. it is possible to improve lower bounds using the same method.