An adaptive upper bound on the Ramsey numbers $R(3,\dots,3)$
Résumé
Since 2002, the best known upper bound on the Ramsey numbers R n (3) = R(3,. .. , 3) is R n (3) ≤ n!(e − 1/6) + 1 for all n ≥ 4. It is based on the current estimate R 4 (3) ≤ 62. We show here how any closing-in on R 4 (3) yields an improved upper bound on R n (3) for all n ≥ 4. For instance, with our present adaptive bound, the conjectured value R 4 (3) = 51 implies R n (3) ≤ n!(e − 5/8) + 1 for all n ≥ 4.
Domaines
Combinatoire [math.CO]Origine | Fichiers produits par l'(les) auteur(s) |
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