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Search results for: GRUNDY NUMBER
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Lower bound on the domination number of a tree.
PublicationW pracy przedstawiono dolne ograniczenie na liczbę dominowania w drzewach oraz przedstawiono pełną charakterystykę grafów ekstremalnych.
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Coronas and Domination Subdivision Number of a Graph
PublicationIn this paper, for a graph G and a family of partitions P of vertex neighborhoods of G, we define the general corona G ◦P of G. Among several properties of this new operation, we focus on application general coronas to a new kind of characterization of trees with the domination subdivision number equal to 3.
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On domination multisubdivision number of unicyclic graphs
PublicationThe paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009), 622–628], we constructively characterize all connected unicyclic graphs with...
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The convex domination subdivision number of a graph
PublicationLet G = (V;E) be a simple graph. A set D\subset V is a dominating set of G if every vertex in V - D has at least one neighbor in D. The distance d_G(u, v) between two vertices u and v is the length of a shortest (u, v)-path in G. An (u, v)-path of length d_G(u; v) is called an (u, v)-geodesic. A set X\subset V is convex in G if vertices from all (a, b)-geodesics belong to X for any two vertices a, b \in X. A set X is a convex dominating...
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Complexity Issues on of Secondary Domination Number
PublicationIn this paper we study the computational complexity issues of the problem of secondary domination (known also as (1, 2)-domination) in several graph classes. We also study the computational complexity of the problem of determining whether the domination and secondary domination numbers are equal. In particular, we study the influence of triangles and vertices of degree 1 on these numbers. Also, an optimal algorithm for finding...
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On some Zarankiewicz numbers and bipartite Ramsey Numbers for Quadrilateral
PublicationThe Zarankiewicz number z ( m, n ; s, t ) is the maximum number of edges in a subgraph of K m,n that does not contain K s,t as a subgraph. The bipartite Ramsey number b ( n 1 , · · · , n k ) is the least positive integer b such that any coloring of the edges of K b,b with k colors will result in a monochromatic copy of K n i ,n i in the i -th color, for some i , 1 ≤ i ≤ k . If n i = m for all i , then we denote this number by b k ( m )....
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Thermo-mechanical reclaiming of ground tire rubber via extrusion at low temperature: Efficiency and limits
PublicationThermomechanical reclaiming of ground tire rubber (GTR) was performed at different temperatures (60, 120, and 180°C) using a co-rotating twin-screw extruder. Obtained samples were used in styrene-butadiene rubber (SBR) blends. As reference samples, SBR compounds containing untreated GTR were used. Curing characteristics, static and dynamic mechanical properties, and morphology of the obtained blends were determined. The results...
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Polyurethane/ground tire rubber composite foams based on polyglycerol: processing, mechanical and thermal properties
PublicationDuring the synthesis of rigid polyurethane foams, petrochemical polyol was substituted with polyglycerol, the product of thermo-catalytic polycondensation of waste glycerol, resulting from biodiesel production. Two types of ground tire rubbers, untreated and thermo-mechanically reclaimed, were used to obtain ‘‘green’’ polyurethane-polyglycerol composite foams. Samples were prepared by a single-step method for the ratio of NCO/OH...
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Morphology and properties of recycled polyethylene/ground tyre rubber/thermoplastic poly(ester-urethane) blends
PublicationThe growing amount of plastics waste produced every year resulted in development of mechanical and chemical recycling methods of polymers and their blends or composites. From the environmental point of view, the possibility of plastics waste reusing and recycling is desirable. In this study three polymer blends were obtained with using recycled polyethylene (RPE), ground tyre rubber (GTR) and thermoplastic poly(ester-urethane)...
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Synergistic Effects of Bitumen Plasticization and Microwave Treatment on Short-Term Devulcanization of Ground Tire Rubber
PublicationGround tire rubber (GTR) was mechano-chemically modified with road bitumen 160/220 and subsequently treated using a microwave radiation. The combined impact of bitumen 160/220 content and microwave treatment on short-term devulcanization of GTR was studied by thermal camera, wavelength dispersive X-ray fluorescence spectrometry (WD-XRF), static headspace, and gas chromatography-mass spectrometry (SHS-GC-MS), thermogravimetric analysis...
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Insights into Stoichiometry Adjustments Governing the Performance of Flexible Foamed Polyurethane/Ground Tire Rubber Composites
PublicationPolyurethanes (PU) are widely applied in the industry due to their tunable performance adjusted by changes in the isocyanate index—stoichiometric balance between isocyanate and hydroxyl groups. This balance is affected by the incorporation of modifiers of fillers into the PU matrix and is especially crucial for PU foams due to the additional role of isocyanates—foaming of the material. Despite the awareness of the issue underlined...
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Grafting and reactive extrusion technologies for compatibilization of ground tyre rubber composites: Compounding, properties, and applications
PublicationChemical modification of ground tyre rubber (GTR) to compatibilize it with the matrix is a well-known approach. Based on our recent review of the surface etching methods used in GTR modification, the purpose of the current work is to take a deeper look into more advanced methods such as grafting and reactive extrusion. While grafting is more efficient in achieving compatibility, however, it usually involves multi-step synthesis...
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Ground tire rubber thermo-mechanically devulcanized in the presence of waste engine oil as asphalt modifier
PublicationCross-linked elastomers network is main limitation for industrial usage of ground tire rubber (GTR) as asphalts’ and road pavements modifier. GTR was thermo-mechanically devulcanized via extrusion in the presence of waste engine oil (WEO) at temperature ranges from 150 to 280 °C. Combined impact of WEO content and extruder barrel temperature on the change of cross-linked structure of degraded GTR (DTGR) was investigated through...
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The Input of Nanoclays to the Synergistic Flammability Reduction in Flexible Foamed Polyurethane/Ground Tire Rubber Composites
PublicationCurrently, postulated trends and law regulations tend to direct polymer technology toward sustainability and environmentally friendly solutions. These approaches are expressed by keeping materials in a loop aimed at the circular economy and by reducing the environmental burdens related to the production and use of polymers and polymer-based materials. The application of recycled or waste-based materials often deals efficiently...
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Non-standard binary weighted number systems
PublicationZdefiniowano szeroką klasę binarnych systemów wagowych. Wszystkie sa wzajemnie jednoznaczne ale mogą być zupełne lub niezupełne. Jeżeli wagi systemu są kolejnymi liczbami naturalnymi to system jest minimalny.Jesli wagi sa kolejnymi potęgami podstawy Z to system jest maksymalny. W przestrzeni między tymi systemami znajdują się inne systemy binarne. Kilka z nich przedstawiono w referacie.
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Bounds on the vertex-edge domination number of a tree
PublicationA vertex-edge dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every edge of $G$ is incident with a vertex of $D$ or a vertex adjacent to a vertex of $D$. The vertex-edge domination number of a graph $G$, denoted by $\gamma_{ve}(T)$, is the minimum cardinality of a vertex-edge dominating set of $G$. We prove that for every tree $T$ of order $n \ge 3$ with $l$ leaves and $s$ support vertices we have $(n-l-s+3)/4...
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Influence of edge subdivision on the convex domination number
PublicationWe study the influence of edge subdivision on the convex domination number. We show that in general an edge subdivision can arbitrarily increase and arbitrarily decrease the convex domination number. We also find some bounds for unicyclic graphs and we investigate graphs G for which the convex domination number changes after subdivision of any edge in G.
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Lower bound on the paired domination number of a tree
PublicationW pracy przedstawione jest ograniczenie dolne dla liczby dominowania parami oraz scharakteryzowane są wszystkie drzewa ekstremalne.
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Empirical Probability Distributions with Unknown Number of Components
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Graphs with convex domination number close to their order
PublicationW pracy opisane są grafy z liczbą dominowania wypukłego bliską ilości ich wierzchołków.
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Entanglement and Nonlocality are Inequivalent for Any Number of Parties
PublicationUnderstanding the relation between nonlocality and entanglement is one of the fundamental problems in quantum physics. In the bipartite case, it is known that these two phenomena are inequivalent, as there exist entangled states of two parties that do not violate any Bell inequality. However, except for a single example of an entangled three-qubit state that has a local model, almost nothing is known about such a relation in multipartite...
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Weakly convex domination subdivision number of a graph
PublicationA set X is weakly convex in G if for any two vertices a; b \in X there exists an ab–geodesic such that all of its vertices belong to X. A set X \subset V is a weakly convex dominating set if X is weakly convex and dominating. The weakly convex domination number \gamma_wcon(G) of a graph G equals the minimum cardinality of a weakly convex dominating set in G. The weakly convex domination subdivision number sd_wcon (G) is the minimum...
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On the super domination number of lexicographic product graphs
PublicationThe neighbourhood of a vertexvof a graphGis the setN(v) of all verticesadjacent tovinG. ForD⊆V(G) we defineD=V(G)\D. A setD⊆V(G) is called a super dominating set if for every vertexu∈D, there existsv∈Dsuch thatN(v)∩D={u}. The super domination number ofGis theminimum cardinality among all super dominating sets inG. In this article weobtain closed formulas and tight bounds for the super dominating number oflexicographic product...
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T-colorings, divisibility and circular chromatic number
PublicationLet T be a T-set, i.e., a finite set of nonnegative integers satisfying 0 ∈ T, and G be a graph. In the paper we study relations between the T-edge spans espT (G) and espd⊙T (G), where d is a positive integer and d ⊙ T = {0 ≤ t ≤ d (max T + 1): d |t ⇒ t/d ∈ T} . We show that espd⊙T (G) = d espT (G) − r, where r, 0 ≤ r ≤ d − 1, is an integer that depends on T and G. Next we focus on the case T = {0} and show that espd⊙{0} (G) =...
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Investigation of volatile low molecular weight compounds formed during continuous reclaiming of ground tire rubber
PublicationGround tire rubber was thermo-mechanically reclaimed at different temperature conditions (80, 120, 160 °C) using a co-rotating twin screw extruder. The progress of ground tire rubber reclaiming was evaluated with specific mechanical energy, sol fraction and thermogravimetric analysis. Volatile organic compounds (VOCs) including volatile sulfur compounds (VCSs) released from ground tire rubber and ground tire rubber after reclaiming...
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Curing characteristics, mechanical and thermal properties of reclaimed ground tire rubber cured with various vulcanizing systems
PublicationGround tire rubber was thermo-mechanical reclaimed at 120 °C using a co-rotating twin screw extruder. The effect of vulcanizing system type on curing characteristics, static mechanical properties (tensile strength, elongation-at-break, hardness and resilience), dynamic mechanical properties and thermal properties of reclaimed ground tire rubber was investigated. Reclaimed rubber was cured using different types of vulcanization...
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Thermo-oxidative exfoliation of carbon black from ground tire rubber as potential reinforcement in green tires
PublicationConsidering the balance between rapidly growing global tire demand and scarcity of natural resources, recycling and reclaiming techniques of tire rubber have become the state of the art. Herein, we set out to implement a self-designed thermo-oxidative reactor for the exfoliation of carbon black (CB) from ground tire rubber, which is efficiently functioned under a thermo-oxidative reclaiming condition without any additive. The exfoliation...
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The Impact of Hybrid Flame Retardant Compositions on the Performance of Foamed Flexible Polyurethane/Ground Tire Rubber Composites
PublicationCurrent sustainability-oriented trends affect polyurethane (PU) materials and stimulate the incorporation of recycled or waste-based materials as fillers. Ground tire rubber (GTR) poses as an auspicious candidate due to the excellent performance of car tires. Despite the benefits related to the mechanical performance, it contributes to the increasing flammability of the resulting composites. Herein, presented work assessed the...
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The Impact of Isocyanate Index and Filler Functionalities on the Performance of Flexible Foamed Polyurethane/Ground Tire Rubber Composites
PublicationThe structure and performance of polyurethane (PU) foams are strongly driven by the stoichiometry of the polyaddition reaction, quantitatively described by the isocyanate index. It determines the balance between isocyanate and hydroxyl groups in the reacting system and is affected by the introduction of additional functionalities originated, e.g., from applied fillers. Nevertheless, this issue is hardly taken into account in research...
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Polyhedral Ramsey Numbers
PublicationGiven two polygons or polyhedrons P1 and P2, we can transform these figures to graphs G1 and G2, respectively. The polyhedral Ramsey number Rp(G1,G2) is the smallest integer n such that every graph, which represents polyhedron on n vertices either contains a copy of G1 or its complement contains a copy of G2. Using a computer search together with some theoretical results we have established some polyhedral Ramsey numbers, for example...
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Nordhaus-Gaddum results for the convex domination number of a graph
PublicationPraca dotyczy nierówności typu Nordhausa-Gadduma dla dominowania wypukłego.
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improved noniterative residue division for small number ranges
Publicationw pracy zaprezentowano multiplikatywny algorytm dzielenia w systemie resztowym i projekt 12-bitowego dzielnika dla modułów 5-bitowych. w algorytmie zastosowano obliczanie przybliżonej odwrotności dzielnika i mnozenie przez dzielną. binarna reprezentacja dzielnika jest dekomponowana na dwa segmenty 6-bitowe, co umożliwia obliczenie w środowisku fpga poprzez odwzorowanie realizowane jako odczyt pamięci. w pracy podano udoskonalony...
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On the independence number of some strong products of cycle-powers
PublicationIn the paper we give some theoretical and computational results on the third strong power of cycle-powers, for example, we have found the independence numbers alpha((C^2_10)^⊠3) = 30 and alpha((C^4 _14)^⊠3) = 14. A number of optimizations have been introduced to improve the running time of our exhaustive algorithm used to establish the independence number of the third strong power of cycle-powers. Moreover, our results establish...
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On trees attaining an upper bound on the total domination number
PublicationA total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. The total domination number of a graph G, denoted by γ_t(G), is the minimum cardinality of a total dominating set of G. Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International Journal of Graphs and Combinatorics 1 (2004), 69-75] established the following upper bound on the total domination...
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Lower bound on the weakly connected domination number of a tree
PublicationPraca dotyczy dolnego ograniczenia liczby dominowania słabo spójnego w drzewach (ograniczenie ze względu na ilość wierzchołków i ilość wierzchołków końcowych w drzewie).
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The Dependence of Electrode Impedance on the Number of Performed EEG Examinations
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Complex multiplier based on the polynomial residue number system
PublicationPrzedstawiono próbę zaprojektowania mnożnika zespolonego 4x4 opartego na algorytmie Skavantzosa i Stouraitisa. W algorytmie stosuje siękodowanie liczb n-bitowych jako wielomianów stopnia 7 w pierścieniu wielomianów modulo (x^8-1) z n/4-bitowymi współczynnikami. Mnożenie zespolone jest wykonywane jako 8-punktowy splot cykliczny. Podanoopóżnienie i złożoność sprzętową jak również porównanie ze standardowym.rozwiązaniem.
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Lower bound on the distance k-domination number of a tree
PublicationW artykule przedstawiono dolne ograniczenie na liczbę k-dominowania w drzewach oraz scharakteryzowano wszystkie grafy ekstremalne.
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Computation of the convolution with use of the polynomial residue number system.
PublicationPrzedstawiono użycie wielomianowych systemów resztowych do obliczania splotu w cyfrowych układach dużej skali integracji VLSI.
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Block graphs with large paired domination multisubdivision number
PublicationThe paired domination multisubdivision number of a nonempty graph G, denoted by msdpr(G), is the smallest positive integer k such that there exists an edge which must be subdivided k times to increase the paired domination number of G. It is known that msdpr(G) ≤ 4 for all graphs G. We characterize block graphs with msdpr(G) = 4.
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Local Nusselt number evaluation in the case of jet impingement
PublicationJet impingement still is one of demanding cases regarding computational fluid dynamics, due to its highly turbulent behaviour, with occurrence of turbulent-laminar transition. Even recently developed methods exhibit some drawbacks – RANS based simulations lack accuracy, LES and DNS based ones require too much computational time. Hybrid methods also exist, but their development and validation is in progress. Nevertheless, CFD application...
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Paired domination versus domination and packing number in graphs
PublicationGiven a graph G = (V(G), E(G)), the size of a minimum dominating set, minimum paired dominating set, and a minimum total dominating set of a graph G are denoted by γ (G), γpr(G), and γt(G), respectively. For a positive integer k, a k-packing in G is a set S ⊆ V(G) such that for every pair of distinct vertices u and v in S, the distance between u and v is at least k + 1. The k-packing number is the order of a largest kpacking and...
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Graphs with isolation number equal to one third of the order
PublicationA set D of vertices of a graph G is isolating if the set of vertices not in D and with no neighbor in D is independent. The isolation number of G, denoted by \iota(G) , is the minimum cardinality of an isolating set of G. It is known that \iota(G) \leq n/3 , if G is a connected graph of order n, , distinct from C_5 . The main result of this work is the characterisation of unicyclic and block graphs of order n with isolating number...
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Efficiency of thermomechanical reclaiming of ground tire rubber conducted in counter-rotating and co-rotating twin screw extruder
PublicationIn this article the results of research on a continuous thermomechanical reclaiming process of ground tire rubber (GTR) conducted in a twin screw extruder are presented. The effects of the rotation direction (co-rotating/counter-rotating), design of co-rotating plasticizing units and the rotational speed of the screws on the extruder working parameters, sol fraction and the degree of reclaiming in the obtained products were described....
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Investigating the combined impact of plasticizer and shear force on the efficiency of low temperature reclaiming of ground tire rubber (GTR)
PublicationIn the present work, ground tire rubber (GTR) was mechano-chemically reclaimed at ambient temperature using two-roll mills. Road bitumen and styrene-butadiene-styrene (SBS)-modified bitumen at variable content (in range: 2.5–20 phr) were applied as reactive plasticizers to enhance reclaiming of GTR. For better understanding the plasticizing effect of bitumen on the quality of obtained reclaimed rubber, mechano-chemically reclaimed...
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Effect of Compounding Conditions on Static and Dynamic Mechanical Properties of High Density Polyethylene/Ground Tire Rubber Blends
PublicationSearching for new and cost-effective methods of waste rubber recycling is a subject of research in many scientific centers in the world. In this paper there are presented results of the research of the extrusion process of cheap and environmentally friendly thermoplastic compositions containing 50 % wt. of masses of ground tire rubber (GTR). The aim of this study was to determine the relationship between the mixing conditions and...
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Use of response surface methodology in characterization of properties of recycled high density polyethylene/ground tire rubber compositions
PublicationSearching for newways to utilize rubber and polymerwaste has been the focus of many studies conducted by research centers and companies worldwide. In this study, the influence of extrusion conditions on the properties of thermoplastic compositions containing post-production recycled high density polyethylene (PE-HD) and ground tire rubber (GTR) at 50:50 mass ratiowas examined. Response Surface Methodology (RSM) was used to determine...
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Chemical surface etching methods for ground tire rubber as sustainable approach for environmentally-friendly composites development– a review
PublicationGround tire rubber (GTR) has been used as a sustainable low-cost modifier in various composites. However, due to the hydrophobic nature of GTR, it is in compatible with most matrices and results in deterioration in both mechanical and physical properties of composites. This necessitates pre-modification of the powdered rubber to improve the interfacial bonding at the rubber-matric interface. The most common GTR modification research...
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Structural Changes and Their Implications in Foamed Flexible Polyurethane Composites Filled with Rapeseed Oil-Treated Ground Tire Rubber
PublicationThe utilization of post-consumer car tires is an essential issue from an ecological andeconomic point of view. One of the simplest and the least harmful methods is their material recyclingresulting in ground tire rubber (GTR), which can be further applied as fillers for polymer-basedcomposites. Nevertheless, insufficient interfacial interactions implicate the necessity of GTR modi-fication before introduction into polymer matrices....
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Shannon Capacity and Ramsey Numbers
PublicationRamsey-type theorems are strongly related to some results from information theory. In this paper we present these relations.