scholarly journals On Berge-Ramsey Problems

10.37236/8775 ◽  
2020 ◽  
Vol 27 (2) ◽  
Author(s):  
Dániel Gerbner
Keyword(s):  
Lower Bounds ◽  
Upper Bound ◽  
Constant Term ◽  
Ramsey Number ◽  
Uniform Hypergraph ◽  
Large Margin

Given a graph $G$, a hypergraph $\mathcal{H}$ is a Berge copy of $F$ if $V(G)\subset V(\mathcal{H})$ and there is a bijection $f:E(G)\rightarrow E(\mathcal{H})$ such that for any edge $e$ of $G$ we have $e\subset f(e)$. We study Ramsey problems for Berge copies of graphs, i.e. the smallest number of vertices of a complete $r$-uniform hypergraph, such that if we color the hyperedges with $c$ colors, there is a monochromatic Berge copy of $G$. We obtain a couple results regarding these problems. In particular, we determine for which $r$ and $c$ the Ramsey number can be super-linear. We also show a new way to obtain lower bounds, and improve the general lower bounds by a large margin. In the specific case $G=K_n$ and $r=2c-1$, we obtain an upper bound that is sharp besides a constant term, improving earlier results.

scholarly journals Ramsey numbers for certain k-graphs

1981 ◽  
Vol 30 (3) ◽  
pp. 284-296 ◽  
Author(s):  
Stefan A. Burr ◽  
Richard A. Duke
Keyword(s):  
Lower Bounds ◽  
Complete Solution ◽  
Ramsey Number ◽  
Upper And Lower Bounds ◽  
Uniform Hypergraph ◽  
Steiner Systems ◽  
Ramsey Numbers ◽  
Existence Question

AbstractWe are interested here in the Ramsey number r(T, C), where C is a complete k-uniform hypergraph and T is a “tree-like” k-graph. Upper and lower bounds are found for these numbers which lead, in some cases, to the exact value for r(T, C) and to a generalization of a theorem of Chváta1 on Ramsey numbers for graphs. In other cases we show that a determination of the exact values of r(T, C) would be equivalent to obtaining a complete solution to existence question for a certain class of Steiner systems.

scholarly journals A linear upper bound in zero-sum Ramsey theory

1994 ◽  
Vol 17 (3) ◽  
pp. 609-612 ◽  
Author(s):  
Yair Caro
Keyword(s):  
Upper Bound ◽  
Ramsey Theory ◽  
Ramsey Number ◽  
Uniform Hypergraph ◽  
Zero Sum ◽  
Positive Integers

Letn,randkbe positive integers such thatk|(nr). There exists a constantc(k,r)such that for fixedkandrand for every groupAof orderkR(Knr,A)≤n+c(k,r),whereR(Knr,A)is the zero-sum Ramsey number introduced by Bialostocki and Dierker [1], andKnris the completer-uniform hypergraph onn-vertices.

Improved Bounds for the Ramsey Number of Tight Cycles Versus Cliques

2016 ◽  
Vol 25 (5) ◽  
pp. 791-796
Author(s):  
DHRUV MUBAYI
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Strong Form ◽  
Ramsey Number ◽  
Uniform Hypergraph ◽  
Vertex Set ◽  
Image Position

The 3-uniform tight cycle Cs3 has vertex set ${\mathbb Z}_s$ and edge set {{i, i + 1, i + 2}: i ∈ ${\mathbb Z}_s$}. We prove that for every s ≢ 0 (mod 3) with s ⩾ 16 or s ∈ {8, 11, 14} there is a cs > 0 such that the 3-uniform hypergraph Ramsey number r(Cs3, Kn3) satisfies $$\begin{equation*} r(C_s^3, K_n^3)< 2^{c_s n \log n}.\ \end{equation*}$$ This answers in a strong form a question of the author and Rödl, who asked for an upper bound of the form $2^{n^{1+\epsilon_s}}$ for each fixed s ⩾ 4, where εs → 0 as s → ∞ and n is sufficiently large. The result is nearly tight as the lower bound is known to be exponential in n.

Localization of Discrete Spectrum of Multiparticle Schrödinger Operators

1985 ◽  
Vol 40 (10) ◽  
pp. 1052-1058 ◽  
Author(s):  
Heinz K. H. Siedentop
Keyword(s):  
Discrete Spectrum ◽  
Lower Bounds ◽  
Upper Bound ◽  
Schrödinger Operators ◽  
Upper And Lower Bounds ◽  
Schrodinger Operators

An upper bound on the dimension of eigenspaces of multiparticle Schrödinger operators is given. Its relation to upper and lower bounds on the eigenvalues is discussed.

scholarly journals On the Interactive Capacity of Finite-State Protocols

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 17
Author(s):  
Assaf Ben-Yishai ◽  
Young-Han Kim ◽  
Rotem Oshman ◽  
Ofer Shayevitz
Keyword(s):  
Lower Bounds ◽  
Upper Bound ◽  
Noisy Channel ◽  
Shannon Capacity ◽  
Finite State

The interactive capacity of a noisy channel is the highest possible rate at which arbitrary interactive protocols can be simulated reliably over the channel. Determining the interactive capacity is notoriously difficult, and the best known lower bounds are far below the associated Shannon capacity, which serves as a trivial (and also generally the best known) upper bound. This paper considers the more restricted setup of simulating finite-state protocols. It is shown that all two-state protocols, as well as rich families of arbitrary finite-state protocols, can be simulated at the Shannon capacity, establishing the interactive capacity for those families of protocols.

scholarly journals Encoding Two-Dimensional Range Top-k Queries

Algorithmica ◽  
2021 ◽  
Author(s):  
Seungbum Jo ◽  
Rahul Lingala ◽  
Srinivasa Rao Satti
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Upper Bound ◽  
Total Order ◽  
Two Dimensional ◽  
Information Theoretic ◽  
Cartesian Tree ◽  
Dimensional Range

AbstractWe consider the problem of encoding two-dimensional arrays, whose elements come from a total order, for answering $${\text{Top-}}{k}$$ Top- k queries. The aim is to obtain encodings that use space close to the information-theoretic lower bound, which can be constructed efficiently. For an $$m \times n$$ m × n array, with $$m \le n$$ m ≤ n , we first propose an encoding for answering 1-sided $${\textsf {Top}}{\text {-}}k{}$$ Top - k queries, whose query range is restricted to $$[1 \dots m][1 \dots a]$$ [ 1 ⋯ m ] [ 1 ⋯ a ] , for $$1 \le a \le n$$ 1 ≤ a ≤ n . Next, we propose an encoding for answering for the general (4-sided) $${\textsf {Top}}{\text {-}}k{}$$ Top - k queries that takes $$(m\lg {{(k+1)n \atopwithdelims ()n}}+2nm(m-1)+o(n))$$ ( m lg ( k + 1 ) n n + 2 n m ( m - 1 ) + o ( n ) ) bits, which generalizes the joint Cartesian tree of Golin et al. [TCS 2016]. Compared with trivial $$O(nm\lg {n})$$ O ( n m lg n ) -bit encoding, our encoding takes less space when $$m = o(\lg {n})$$ m = o ( lg n ) . In addition to the upper bound results for the encodings, we also give lower bounds on encodings for answering 1 and 4-sided $${\textsf {Top}}{\text {-}}k{}$$ Top - k queries, which show that our upper bound results are almost optimal.

scholarly journals The Essential Dimension of Stacks of Parabolic Vector Bundles over Curves

2012 ◽  
Vol 10 (3) ◽  
pp. 455-488 ◽  
Author(s):  
Indranil Biswas ◽  
Ajneet Dhillon ◽  
Nicole Lemire
Keyword(s):  
Lower Bounds ◽  
Upper Bound ◽  
Vector Bundles ◽  
Upper Bounds ◽  
Essential Dimension ◽  
Parabolic Structure ◽  
Moduli Stack

AbstractWe find upper bounds on the essential dimension of the moduli stack of parabolic vector bundles over a curve. When there is no parabolic structure, we improve the known upper bound on the essential dimension of the usual moduli stack. Our calculations also give lower bounds on the essential dimension of the semistable locus inside the moduli stack of vector bundles of rank r and degree d without parabolic structure.

scholarly journals A Study on f Number of Points for Number of Points with Inter-Distance of Less Than, or for Number of Points with Inter-Distance of or More to Necessarily Exist on Plane

2018 ◽  
Author(s):  
Benjamin Smith
Keyword(s):  
Upper Bound ◽  
Ramsey Number ◽  
Minimum Value ◽  
Special Case

We defined number of points with an inter-distance of β or more to necessarily exist on a plane. Furthermore, we aimed to reduce the range of this minimum value. We first showed that the upper bound of this value could be scaled by , and further reduced the constant that was multiplied. We compared the upper bound of and the Ramsey number in a special case and confirmed that was a better upper bound than except when were both small or trivial.

scholarly journals On the Rank of $p$-Schemes

10.37236/3097 ◽  
2013 ◽  
Vol 20 (2) ◽  
Author(s):  
Fateme Raei Barandagh ◽  
Amir Rahnamai Barghi
Keyword(s):  
Lower Bound ◽  
Prime Number ◽  
Lower Bounds ◽  
Upper Bound ◽  
Upper And Lower Bounds ◽  
Minimum Rank

Let $n>1$ be an integer and $p$ be a prime number. Denote by $\mathfrak{C}_{p^n}$ the class of non-thin association $p$-schemes of degree $p^n$. A sharp upper and lower bounds on the rank of schemes in $\mathfrak{C}_{p^n}$ with a certain order of thin radical are obtained. Moreover, all schemes in this class whose rank are equal to the lower bound are characterized and some schemes in this class whose rank are equal to the upper bound are constructed. Finally, it is shown that the scheme with minimum rank in $\mathfrak{C}_{p^n}$ is unique up to isomorphism, and it is a fusion of any association $p$-schemes with degree $p^n$.

scholarly journals Branch and Bound Method to Solve Multi Objectives Function

2016 ◽  
Vol 12 (3) ◽  
pp. 5964-5974
Author(s):  
Tahani Jabbar Kahribt ◽  
Mohammed Kadhim Al- Zuwaini
Keyword(s):  
Lower Bounds ◽  
Branch And Bound ◽  
Single Machine ◽  
Upper Bound ◽  
Completion Time ◽  
Heuristic Method ◽  
Total Weighted Completion Time ◽  
Branch And Bound Method ◽  
Special Cases ◽  
Weighted Completion Time

This paper  presents  a  branch  and  bound  algorithm  for  sequencing  a  set  of  n independent  jobs  on  a single  machine  to  minimize sum of the discounted total weighted completion time and maximum lateness,  this problems is NP-hard. Two lower bounds were proposed and heuristic method to get an upper bound. Some special cases were  proved and some dominance rules were suggested and proved, the problem solved with up to 50 jobs.

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