Tighter Bounds on Directed Ramsey Number R(7)
نویسندگان
چکیده
Tournaments are orientations of the complete graph. The directed Ramsey number R(k) is minimum vertices a tournament must have to be guaranteed contain transitive subtournament size k, which we denote by $$ TT _k$$ . We include computer-assisted proof conjecture Sanchez-Flores in Graphs Combinatorics 14(2), 181–200 (1998), that all _6$$ -free tournaments on 24 and 25 subtournaments ST _{27}$$ , unique largest tournament. also classify 23 vertices. use these results, combined with assistance from SAT solver, obtain following improved bounds R(7): $$34 \le R(7) 47$$
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2022
ISSN: ['1435-5914', '0911-0119']
DOI: https://doi.org/10.1007/s00373-022-02560-5