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 $n\geq \Big\lfloor\frac{5m}{4}\Big\rfloor$, we...

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Bibliographic Details
Published in:The Electronic journal of combinatorics 2013-01, Vol.20 (1)
Main Authors: Maherani, Leila, Omidi, Gholam Reza, Raeisi, Ghaffar, Shahsiah, Maryam
Format: Article
Language:English
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Summary: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 $$R(\mathcal{P}^3_n,\mathcal{P}^3_m)=2n+\Big\lfloor\frac{m+1}{2}\Big\rfloor.$$
ISSN:1077-8926
1077-8926
DOI:10.37236/2725