One More Turán Number and Ramsey Number for the Loose 3-Uniform Path of Length Three

• Autorzy: Joanna Polcyn
• Języki publikacji: EN

Abstrakty

EN

Let P denote a 3-uniform hypergraph consisting of 7 vertices a, b, c, d, e, f, g and 3 edges {a, b, c}, {c, d, e}, and {e, f, g}. It is known that the r-color Ramsey number for P is R(P; r) = r + 6 for r ≤ 9. The proof of this result relies on a careful analysis of the Turán numbers for P. In this paper, we refine this analysis further and compute the fifth order Turán number for P, for all n. Using this number for n = 16, we confirm the formula R(P; 10) = 16.

Słowa kluczowe

EN

Ramsey numbers; Turán numbers

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2017
• Tom: 37
• Numer: 2
• Strony: 443-464

Daty

wydano

2017-05-01

otrzymano

2015-12-28

poprawiono

2016-05-09

zaakceptowano

2016-05-09

online

2017-04-01

Twórcy

autor

Joanna Polcyn

• Adam Mickiewicz University Poznań,

Identyfikatory

DOI

10.7151/dmgt.1940