On the monochromatic Schur Triples type problem

2008/01/05 by Thanatipanonda, Thotsaporn "Aek"
#05D10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.0801.0798

Abstract

We discuss a problem posed by Ronald Graham about the minimum number, over all 2-colorings of [1,n], of monochromatic \x,y,x+ay\ triples for a ≥ 1. We give a new proof of the original case of a=1. We show that the minimum number of such triples is at most (n²)/(2a(a²+2a+3)) + O(n) when a ≥ 2. We also find a new upper bound for the minimum number, over all r-colorings of [1,n], of monochromatic Schur triples, for r ≥ 3.

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