Wyniki wyszukiwania dla: on-line ramsey number

• A NOTE ON ON-LINE RAMSEY NUMBERS FOR QUADRILATERALS

  Publikacja

  • J. Cyman
  • T. Dzido

  - Opuscula Mathematica - Rok 2014

  We consider on-line Ramsey numbers defined by a game played between two players, Builder and Painter. In each round Builder draws an the edge and Painter colors it either red or blue, as it appears. Builder’s goal is to force Painter to create a monochromatic copy of a fixed graph H in as few rounds as possible. The minimum number of rounds (assuming both players play perfectly) is the on-line Ramsey number \widetilde{r}(H) of...

  Pełny tekst do pobrania w portalu

• On-line Ramsey Numbers of Paths and Cycles

  Publikacja

  • J. Cyman
  • T. Dzido
  • J. Lapinskas
  • A. Lo

  - ELECTRONIC JOURNAL OF COMBINATORICS - Rok 2015

  Consider a game played on the edge set of the infinite clique by two players, Builder and Painter. In each round, Builder chooses an edge and Painter colours it red or blue. Builder wins by creating either a red copy of $G$ or a blue copy of $H$ for some fixed graphs $G$ and $H$. The minimum number of rounds within which Builder can win, assuming both players play perfectly, is the \emph{on-line Ramsey number} $\tilde{r}(G,H)$. In...

  Pełny tekst do pobrania w portalu

• Application of Regression Line to Obtain Specified Number of Points in Reduced Large Datasets

  Publikacja

  • W. Blaszczak-Bak
  • A. Sobieraj-Żłobińska

  - Rok 2016

  Modern measurement techniques like scanning technology or sonar measurements, provide large datasets, which are a reliable source of information about measured object, however such datasets are sometimes difficult to develop. Therefore, the algorithms for reducing the number of such sets are incorporated into their processing. In the reduction algorithms based on the...

  Pełny tekst do pobrania w serwisie zewnętrznym

• Liczby Ramseya on-line dla różnych klas grafów

  Publikacja

  • R. Zakrzewska

  - Rok 2023

  Rozpatrujemy grę rozgrywaną na nieskończonej liczbie wierzchołków, w której każda runda polega na wskazaniu krawędzi przez jednego gracza - Budowniczego oraz pokolorowaniu jej przez drugiego gracza - Malarkę na jeden z dwóch kolorów, czerwony lub niebieski. Celem Budowniczego jest zmuszenie Malarki do stworzenia monochromatycznej kopii wcześniej ustalonego grafu H w jak najmniejszej możliwej liczbie ruchów. Zakładamy, że gracze...

  Pełny tekst do pobrania w portalu

• On some open questions for Ramsey and Folkman numbers

  Publikacja

  • S. Radziszowski
  • X. Xiaodong

  - Rok 2016

  We discuss some of our favorite open questions about Ramsey numbers and a related problem on edge Folkman numbers. For the classical two-color Ramsey numbers, we first focus on constructive bounds for the difference between consecutive Ramsey numbers. We present the history of progress on the Ramsey number R(5,5) and discuss the conjecture that it is equal to 43.

• Polyhedral Ramsey Numbers

  Publikacja

  • M. Jurkiewicz

  - Zeszyty Naukowe Wydziału ETI Politechniki Gdańskiej. Technologie Informacyjne - Rok 2011

  Given 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...

• On some Zarankiewicz numbers and bipartite Ramsey Numbers for Quadrilateral

  Publikacja

  • J. Dybizbański
  • T. Dzido
  • S. Radziszowski

  - ARS COMBINATORIA - Rok 2015

  The 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 )....

  Pełny tekst do pobrania w portalu

• Shannon Capacity and Ramsey Numbers

  Publikacja

  • M. Jurkiewicz
  • M. Kubale

  - Rok 2011

  Ramsey-type theorems are strongly related to some results from information theory. In this paper we present these relations.

• Dataset of non-isomorphic graphs of the coloring types (K4,K4;n), 1<n<R(4,4)

  Dane Badawcze

  open access

  • R. Fidytek
  • G. Graff

  For K4 graph, a coloring type (K4,K4;n) is such an edge coloring of the full Kn graph, which does not have the K4 subgraph in the first color (representing by no edges in the graph) or the K4 subgraph in the second color (representing by edges in the graph).The Ramsey number R(4,4) is the smallest natural number n such that for any edge coloring of...

• Dataset of non-isomorphic graphs being coloring types (K5-e,Km-e;n), 2<m<5, 1<n<R(K5-e,Km-e)

  Dane Badawcze

  open access

  • R. Fidytek
  • G. Graff

  For K5-e and Km-e graphs, the type coloring (K5-e,Km-e;n) is such an edge coloring of the full Kn graph, which does not have the K5-e subgraph in the first color (no edge in the graph) or the Km-e subgraph in the second color (exists edge in the graph). Km-e means the full Km graph with one edge removed.The Ramsey number R(K5-e,Km-e) is the smallest...