-
Leila Maherani
-
Gholam Reza Omidi
-
Ghaffar Raeisi
-
Maryam Shahsiah
Keywords:
Ramsey Number, Loose Path, Loose Cycle
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 $$R(\mathcal{P}^3_n,\mathcal{P}^3_m)=2n+\Big\lfloor\frac{m+1}{2}\Big\rfloor.$$