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

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

2021 ◽  
pp. 142-147
Author(s):  
Martin Balko ◽  
Máté Vizer
Keyword(s):  
Ramsey Numbers ◽  
Uniform Hypergraphs

scholarly journals On Ramsey numbers of uniform hypergraphs with given maximum degree

2006 ◽  
Vol 113 (7) ◽  
pp. 1555-1564 ◽  
Author(s):  
A.V. Kostochka ◽  
V. Rödl
Keyword(s):  
Maximum Degree ◽  
Ramsey Numbers ◽  
Uniform Hypergraphs

scholarly journals Degrees in Oriented Hypergraphs and Ramsey p-Chromatic Number

10.37236/2576 ◽  
2012 ◽  
Vol 19 (3) ◽  
Author(s):  
Yair Caro ◽  
Adriana Hansberg
Keyword(s):  
Chromatic Number ◽  
Ramsey Numbers ◽  
Uniform Hypergraphs ◽  
Minimum Cover ◽  
The Family ◽  
Maximum Directed Cut

The family $D(k,m)$ of graphs having an orientation such that for every vertex $v \in V(G)$ either (outdegree) $\deg^+(v) \le k$ or (indegree) $\deg^-(v) \le m$ have been investigated recently in several papers because of the role $D(k,m)$ plays in the efforts to estimate the maximum directed cut in digraphs and the minimum cover of digraphs by directed cuts. Results concerning the chromatic number of graphs in the family $D(k,m)$ have been obtained via the notion of $d$-degeneracy of graphs. In this paper we consider a far reaching generalization of the family $D(k,m)$, in a complementary form, into the context of $r$-uniform hypergraphs, using a generalization of Hakimi's theorem to $r$-uniform hypergraphs and by showing some tight connections with the well known Ramsey numbers for hypergraphs.

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).

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