scholarly journals Anti-Ramsey number of matchings in r-partite r-uniform hypergraphs

2022 ◽  
Vol 345 (4) ◽  
pp. 112782
Author(s):  
Yisai Xue ◽  
Erfang Shan ◽  
Liying Kang
Keyword(s):  
Ramsey Number ◽  
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 The size-Ramsey number of 3-uniform tight paths

2021 ◽  
Author(s):  
Jie Han ◽  
Yoshiharu Kohayakawa ◽  
Shoham Letzter ◽  
Guilherme Oliveira Mota ◽  
Olaf Parczyk
Keyword(s):  
Graph Theory ◽  
Ramsey Number ◽  
Uniform Hypergraphs

Given a hypergraph H, the size-Ramsey number r(H) is the smallest integer m such that there exists a graph G with m edges with the property that in any colouring of the edges of G with two colours there is amonochromatic copy of H. We prove that the size-Ramsey number of the 3-uniform tight path on n vertices P_n is linear in n, i.e., r(P_n)=O(n). This answers a question by Dudek, Fleur, Mubayi, and Rödl for 3-uniform hypergraphs [On the size-Ramsey number of hypergraphs, J. Graph Theory 86 (2016), 417-434], who proved r(P_n)=O(n^1.5*log^1.5 n).

scholarly journals The Ramsey Number of Fano Plane Versus Tight Path

10.37236/8374 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
József Balogh ◽  
Felix Christian Clemen ◽  
Jozef Skokan ◽  
Adam Zsolt Wagner
Keyword(s):  
Edge Coloring ◽  
Ramsey Number ◽  
Short Paper ◽  
Simple Construction ◽  
Uniform Hypergraph ◽  
Fano Plane ◽  
Blue Edge ◽  
Uniform Hypergraphs ◽  
Plane Versus

The hypergraph Ramsey number of two $3$-uniform hypergraphs $G$ and $H$, denoted by $R(G,H)$, is the least integer~$N$ such that every red-blue edge-coloring of the complete $3$-uniform hypergraph on $N$ vertices contains a red copy of $G$ or a blue copy of $H$. The Fano plane $\mathbb{F}$ is the unique 3-uniform hypergraph with seven edges on seven vertices in which every pair of vertices is contained in a unique edge. There is a simple construction showing that $R(H,\mathbb{F}) \ge 2(v(H)-1) + 1.$  Hypergraphs $H$ for which the equality holds are called $\mathbb{F}$-good. Conlon asked to determine all $H$ that are $\mathbb{F}$-good.In this short paper we make progress on this problem and prove that the tight path of length $n$ is $\mathbb{F}$-good.

scholarly journals A Note on On-Line Ramsey Numbers for Some Paths

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 735
Author(s):  
Tomasz Dzido ◽  
Renata Zakrzewska
Keyword(s):  
Ramsey Number ◽  
Ramsey Numbers ◽  
Minimum Number ◽  
On Line ◽  
Infinite Set ◽  
Do So

We consider the important generalisation of Ramsey numbers, namely on-line Ramsey numbers. It is easiest to understand them by considering a game between two players, a Builder and Painter, on an infinite set of vertices. In each round, the Builder joins two non-adjacent vertices with an edge, and the Painter colors the edge red or blue. An on-line Ramsey number r˜(G,H) is the minimum number of rounds it takes the Builder to force the Painter to create a red copy of graph G or a blue copy of graph H, assuming that both the Builder and Painter play perfectly. The Painter’s goal is to resist to do so for as long as possible. In this paper, we consider the case where G is a path P4 and H is a path P10 or P11.

scholarly journals Rainbow matchings for 3-uniform hypergraphs

2021 ◽  
Vol 183 ◽  
pp. 105489
Author(s):  
Hongliang Lu ◽  
Xingxing Yu ◽  
Xiaofan Yuan
Keyword(s):  
Uniform Hypergraphs

scholarly journals New values for the bipartite Ramsey number of the four-cycle versus stars

2021 ◽  
Vol 344 (5) ◽  
pp. 112320
Author(s):  
Imre Hatala ◽  
Tamás Héger ◽  
Sam Mattheus
Keyword(s):  
Ramsey Number

scholarly journals On the size Ramsey number of all cycles versus a path

2021 ◽  
Vol 344 (5) ◽  
pp. 112322
Author(s):  
Deepak Bal ◽  
Ely Schudrich
Keyword(s):  
Ramsey Number

scholarly journals Hypercycle Systems of 5-Cycles in Complete 3-Uniform Hypergraphs

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 484
Author(s):  
Anita Keszler ◽  
Zsolt Tuza
Keyword(s):  
Element Subset ◽  
Uniform Hypergraphs ◽  
Vertex Set ◽  
Recursive Constructions

In this paper, we consider the problem of constructing hypercycle systems of 5-cycles in complete 3-uniform hypergraphs. A hypercycle system C(r,k,v) of order v is a collection of r-uniform k-cycles on a v-element vertex set, such that each r-element subset is an edge in precisely one of those k-cycles. We present cyclic hypercycle systems C(3,5,v) of orders v=25,26,31,35,37,41,46,47,55,56, a highly symmetric construction for v=40, and cyclic 2-split constructions of orders 32,40,50,52. As a consequence, all orders v≤60 permitted by the divisibility conditions admit a C(3,5,v) system. New recursive constructions are also introduced.

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