scholarly journals On Ordered Ramsey Numbers of Tripartite 3-Uniform Hypergraphs

2022 ◽  
Vol 36 (1) ◽  
pp. 214-228
Author(s):  
Martin Balko ◽  
Máté Vizer
Keyword(s):  
Ramsey Numbers ◽  
Uniform Hypergraphs

scholarly journals HYPERGRAPH RAMSEY NUMBERS AND ADIABATIC QUANTUM ALGORITHM

2012 ◽  
Vol 10 (06) ◽  
pp. 1250067 ◽  
Author(s):  
RI QU ◽  
SU-LI ZHAO ◽  
YAN-RU BAO ◽  
XIAO-CHUN CAO
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Quantum Algorithm ◽  
Combinatorial Optimization Problem ◽  
Quantum Evolution ◽  
Ramsey Numbers ◽  
Uniform Hypergraphs

Gaitan and Clark [Phys. Rev. Lett.108 (2012) 010501] have recently presented a quantum algorithm for the computation of the Ramsey numbers R(m, n) using adiabatic quantum evolution (AQE). We consider that the two-color Ramsey numbers R(m, n; r) for r-uniform hypergraphs can be computed by using the similar ways in Phys. Rev. Lett.108 (2012) 010501. In this paper, we show how the computation of R(m, n; r) can be mapped to a combinatorial optimization problem whose solution be found using AQE.

On induced Ramsey numbers fork-uniform hypergraphs

2015 ◽  
Vol 48 (1) ◽  
pp. 5-20
Author(s):  
Domingos Dellamonica ◽  
Steven La Fleur ◽  
Vojtěch Rödl
Keyword(s):  
Ramsey Numbers ◽  
Uniform Hypergraphs

scholarly journals Diagonal Ramsey Numbers of Loose Cycles in Uniform Hypergraphs

2017 ◽  
Vol 31 (3) ◽  
pp. 1634-1669
Author(s):  
G. R. Omidi ◽  
M. Shahsiah
Keyword(s):  
Ramsey Numbers ◽  
Uniform Hypergraphs

Embeddings and Ramsey numbers of sparse κ-uniform hypergraphs

COMBINATORICA ◽  
2009 ◽  
Vol 29 (3) ◽  
pp. 263-297 ◽  
Author(s):  
Oliver Cooley ◽  
Nikolaos Fountoulakis ◽  
Daniela Kühn ◽  
Deryk Osthus
Keyword(s):  
Ramsey Numbers ◽  
Uniform Hypergraphs

scholarly journals 3-Uniform hypergraphs of bounded degree have linear Ramsey numbers

2008 ◽  
Vol 98 (3) ◽  
pp. 484-505 ◽  
Author(s):  
Oliver Cooley ◽  
Nikolaos Fountoulakis ◽  
Daniela Kühn ◽  
Deryk Osthus
Keyword(s):  
Bounded Degree ◽  
Ramsey Numbers ◽  
Uniform Hypergraphs

scholarly journals The Ramsey Number of Loose Paths in 3-Uniform Hypergraphs

10.37236/2725 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
Leila Maherani ◽  
Gholam Reza Omidi ◽  
Ghaffar Raeisi ◽  
Maryam Shahsiah
Keyword(s):  
The Other ◽  
Ramsey Number ◽  
Ramsey Numbers ◽  
Uniform Hypergraphs ◽  
Asymptotic Values

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

The 3-Colour Ramsey Number of a 3-Uniform Berge Cycle

2010 ◽  
Vol 20 (1) ◽  
pp. 53-71 ◽  
Author(s):  
ANDRÁS GYÁRFÁS ◽  
GÁBOR N. SÁRKÖZY
Keyword(s):  
Ramsey Number ◽  
Regularity Lemma ◽  
Ramsey Numbers ◽  
Uniform Hypergraphs

The asymptotics of 2-colour Ramsey numbers of loose and tight cycles in 3-uniform hypergraphs were recently determined [16, 17]. We address the same problem for Berge cycles and for 3 colours. Our main result is that the 3-colour Ramsey number of a 3-uniform Berge cycle of length n is asymptotic to $\frac{5n}{4}$. The result is proved with the Regularity Lemma via the existence of a monochromatic connected matching covering asymptotically 4n/5 vertices in the multicoloured 2-shadow graph induced by the colouring of Kn(3).

scholarly journals On Generalized Ramsey Numbers for 3-Uniform Hypergraphs

2013 ◽  
Vol 76 (3) ◽  
pp. 217-223 ◽  
Author(s):  
Andrzej Dudek ◽  
Dhruv Mubayi
Keyword(s):  
Ramsey Numbers ◽  
Uniform Hypergraphs
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