Geodesic
The Ramsey number of loose paths in 3-uniform hypergraphs
Leila Maherani1 ; Gholam Reza Omidi1 ; Ghaffar Raeisi2 ; Maryam Shahsiah1
1Isfahan University of Technology
2Shahrekord University
The electronic journal of combinatorics, Tome 20 (2013) no. 1
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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 $$R(\mathcal{P}^3_n,\mathcal{P}^3_m)=2n+\Big\lfloor\frac{m+1}{2}\Big\rfloor.$$
DOI : 10.37236/2725
Classification : 05C55, 05C15, 05C65
Mots-clés : Ramsey number, loose path, loose cycle

Leila Maherani  1   ; Gholam Reza Omidi  1   ; Ghaffar Raeisi  2   ; Maryam Shahsiah  1

1 Isfahan University of Technology
2 Shahrekord University 
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     title = {The {Ramsey} number of loose paths in 3-uniform hypergraphs},
     journal = {The electronic journal of combinatorics},
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Leila Maherani; Gholam Reza Omidi; Ghaffar Raeisi; Maryam Shahsiah. The Ramsey number of loose paths in 3-uniform hypergraphs. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2725

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