The Ramsey Number of Loose Paths in 3-Uniform Hypergraphs

Leila Maherani, Gholam Reza Omidi, Ghaffar Raeisi, Maryam Shahsiah

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 $$R(\mathcal{P}^3_n,\mathcal{P}^3_m)=2n+\Big\lfloor\frac{m+1}{2}\Big\rfloor.$$

Keywords


Ramsey Number, Loose Path, Loose Cycle

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