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Tighter Bounds on Directed Ramsey Number R by Neiman, David; Mackey, John; Heule, Marijn is a scholarly article available to read on EtoBox.

What is Tighter Bounds on Directed Ramsey Number R about?

Tournaments are orientations of the complete graph, and the directed Ramsey number $R(k)$ is the minimum number of vertices a tournament must have to be guaranteed to contain a transitive subtournament of size $k$, which we denote by $TT_k$. We include a computer-assisted proof of a conjecture by Sanchez-Flores that all $TT_6$-free tournaments on 24 and 25 vertices are subtournaments of $ST_{27}$, the unique largest TT_6-free tournament. We also classify all $TT_6$-free tournaments on 23 vertices. We use these results, combined with assistance from SAT technology, to obtain the following improved bounds: $34 \leq R(7) \leq 47$.

Author

Neiman, David; Mackey, John; Heule, Marijn

Published

2020

Language

EN