The Ramsey number of loose paths in 3-uniform hypergraphs

2012/09/19 by Leila Maherani, Maherani, Leila, Gholamreza Omidi +5 · 1 citation
Mathematics · Computer Science · #Limits and Structures in Graph Theory #Advanced Topology and Set Theory #Advanced Graph Theory Research

paper · pdf · doi:10.48550/arxiv.1209.4159

Abstract

Recently, asymptotic values of 2-color Ramsey numbers for loose cycles and also loose paths were determined. Here we determine the 2-color Ramsey number of 3-uniform loose paths when one of the paths is significantly larger than the other: for every n≥ \lfloor(5m)/(4)\rfloor, we show that R(P³_n,P³_m)=2n+\lfloor(m+1)/(2)\rfloor.

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• Ramsey numbers of 3-uniform loose paths and loose cycles

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