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The Ramsey number of loose paths in 3-uniform hypergraphs
Published 19 Sep 2012 in math.CO | (1209.4159v3)
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 $n\geq \Big\lfloor\frac{5m}{4}\Big\rfloor$, we show that $$R(\mathcal{P}3_n,\mathcal{P}3_m)=2n+\Big\lfloor\frac{m+1}{2}\Big\rfloor.$$
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