The Ramsey Number of Loose Paths in 3-Uniform Hypergraphs (original) (raw)

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• 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 333-uniform loose paths when one of the paths is significantly larger than the other: for every ngeqBiglfloorfrac5m4Bigrfloorn\geq \Big\lfloor\frac{5m}{4}\Big\rfloorngeqBiglfloorfrac5m4Bigrfloor, 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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How to Cite

Maherani, L., Omidi, G. R., Raeisi, G., & Shahsiah, M. (2013). The Ramsey Number of Loose Paths in 3-Uniform Hypergraphs. The Electronic Journal of Combinatorics, 20(1), #P12. https://doi.org/10.37236/2725