The Ramsey number of loose paths in 3-uniform hypergraphs

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 $n\ge \lfloor \frac{5m}{4}\rfloor$, we show that $$R({\mathcal{P}}_n^3,{\mathcal{P}}_m^3)=2n+\lfloor \frac{m+1}{2}\rfloor \mathrm{.}$$