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

Joanna Polcyn. "One More Turán Number and Ramsey Number for the Loose 3-Uniform Path of Length Three." Discussiones Mathematicae Graph Theory 37.2 (2017): 443-464. <http://eudml.org/doc/287978>.

@article{JoannaPolcyn2017,
abstract = {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.},
author = {Joanna Polcyn},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {Ramsey numbers; Turán numbers},
language = {eng},
number = {2},
pages = {443-464},
title = {One More Turán Number and Ramsey Number for the Loose 3-Uniform Path of Length Three},
url = {http://eudml.org/doc/287978},
volume = {37},
year = {2017},
}

TY - JOUR
AU - Joanna Polcyn
TI - One More Turán Number and Ramsey Number for the Loose 3-Uniform Path of Length Three
JO - Discussiones Mathematicae Graph Theory
PY - 2017
VL - 37
IS - 2
SP - 443
EP - 464
AB - 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.
LA - eng
KW - Ramsey numbers; Turán numbers
UR - http://eudml.org/doc/287978
ER -