Results 91 to 100 of about 1,298 (200)
, 2000 This project has two goals. First, we seek to extend our understanding of Ramsey Graph Theory by examining diagonal Ramsey Numbers and improving their known bound values.
Clark, Benjamin M. +1 more
core
two aspects of Ramsey theory [PDF]
, 2003 In der Ramsey Theorie fuer Graphen haben Burr und Erdos vor nunmehr fast dreissig Jahren zwei Vermutungen formuliert, die sich als richtungsweisend erwiesen haben.
Shi, Lingsheng
core +1 more source
Monochromatic Sums and Products of Polynomials
Discrete AnalysisMonochromatic sums and products of polynomials, Discrete Analysis 2024:5, 7 pp. An early result in Ramsey theory, Schur's theorem, states that if the positive integers are finitely coloured, then there will always be $x$ and $y$ such that $x,y$ and $x ...
Ryan Alweiss
doaj +1 more source
A natural generalisation in graph Ramsey theory
, 2017 In this note we study graphs $G_r$ with the property that every colouring of $E(G_r)$ with $r+1$ colours admits a copy of some graph $H$ using at most $r$ colours. For $1\le r\le e(H)$ such graphs occur naturally at intermediate steps in the synthesis of a $2$-colour Ramsey graph $G_1\longrightarrow H$.
Haupt, Alexander, Reding, Damian
openaire +2 more sources
Ramsey theory and strength of graphs
A numbering $f$ of a graph $G$ of order $n$ is a labeling that assigns distinct elements of the set $\left\{ 1,2,\ldots ,n\right\} $ to the vertices of $G$, where each $uv\in E\left( G\right) $ is labeled $f\left( u\right) +f\left( v\right) $. The strength $\mathrm{str}\left( G\right) $ of $G$ is defined by $\mathrm{str}\left( G\right) =\min \left ...
Ichishima, Rikio +2 more
openaire +2 more sources
Contributions to graph theory [PDF]
, 2005 In this thesis we consider the following three topics in graph theory: spanning 2-connected subgraphs of grid graphs, Ramsey numbers for paths versus other graphs, and some variations of vertex ...
Salman, M.
core
It is always guaranteed to find some order in chaos -- we just need to take a large enough chaos. To explain why, we use the tools from the area of mathematics known as Ramsey theory.
Ermakovich, Elizaveta
core
Efficient DNA Algorithm for Constructing Ramsey Graph based on Minimal Degree Vertex
, 2009 As a famous problem in Combinatorics, small Ramsey number is very hard to solve, because it needs to enumerate all possible graphs in exponential time. We propose a new DNA algorithm for constructing Ramsey graphs, which is a complete process for a small-
Dongming Zhao +5 more
core +1 more source
Fermat Principle, Ramsey Theory and Metamaterials. [PDF]
Materials (Basel), 2023 Frenkel M, Shoval S, Bormashenko E.
europepmc +1 more source