TY - JOUR

T1 - The Ramsey number of the Fano plane versus the tight path

AU - Balogh, József

AU - Clemen, Felix Christian

AU - Skokan, Jozef

AU - Wagner, Adam Zsolt

N1 - Funding Information:
∗and Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprodny, Moscow Region,141701, Russian Federation. Research is partially supported by NSF Grant DMS-1500121, Arnold O. Beckman Research Award (UIUC Campus Research Board RB 18132) and the Langan Scholar Fund (UIUC). †Research has been partially performed while at the University of Illinois at Urbana-Champaign.

PY - 2020

Y1 - 2020

N2 - The hypergraph Ramsey number of two 3-uniform hypergraphs G and H, de-noted by R(G, H), is the least integer N such that every red-blue edge-coloring of the complete 3-uniform hypergraph on N vertices contains a red copy of G or a blue copy of H. The Fano plane F is the unique 3-uniform hypergraph with seven edges on seven vertices in which every pair of vertices is contained in a unique edge. There is a simple construction showing that R(G, F) ≥ 2(v(G) − 1) + 1 for every connected G. Hypergraphs G for which the equality R(G, F) = 2(v(G) − 1) + 1 holds are called F-good. Conlon posed the problem to determine all G that are F-good. In this short paper we make progress on this problem by proving that the tight path of length n is F-good.

AB - The hypergraph Ramsey number of two 3-uniform hypergraphs G and H, de-noted by R(G, H), is the least integer N such that every red-blue edge-coloring of the complete 3-uniform hypergraph on N vertices contains a red copy of G or a blue copy of H. The Fano plane F is the unique 3-uniform hypergraph with seven edges on seven vertices in which every pair of vertices is contained in a unique edge. There is a simple construction showing that R(G, F) ≥ 2(v(G) − 1) + 1 for every connected G. Hypergraphs G for which the equality R(G, F) = 2(v(G) − 1) + 1 holds are called F-good. Conlon posed the problem to determine all G that are F-good. In this short paper we make progress on this problem by proving that the tight path of length n is F-good.

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U2 - 10.37236/8374

DO - 10.37236/8374

M3 - Article

AN - SCOPUS:85085761460

VL - 27

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

SN - 1077-8926

IS - 1

M1 - P1.60

ER -