The Triangle-Free Process and the Ramsey Number R(3,k)

The areas of Ramsey theory and random graphs have been closely linked ever since Erdős's famous proof in 1947 that the ""diagonal"" Ramsey numbers R(k) grow exponentially in k. In the early 1990s, the triangle-free process was introduced as a model which might potentially p...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Pontiveros, Gonzalo Fiz
Otros Autores: Griffiths, Simon, Morris, Robert
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence : American Mathematical Society, 1920.
Colección:Memoirs of the American Mathematical Society Ser.
Temas:
Ramsey theory.
Combinatorial analysis.
Théorie de Ramsey.
Analyse combinatoire.
Combinatorial analysis
Ramsey theory
Probability theory and stochastic processes {For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX} > Combinatorial probability > Combinatorial probability.
Combinatorics {For finite fields, see 11Txx} > Extremal combinatorics > Ramsey theory [See also 05C55].
Combinatorics {For finite fields, see 11Txx} > Extremal combinatorics > Probabilistic methods.
Acceso en línea:Texto completo
Descripción
Sumario:The areas of Ramsey theory and random graphs have been closely linked ever since Erdős's famous proof in 1947 that the ""diagonal"" Ramsey numbers R(k) grow exponentially in k. In the early 1990s, the triangle-free process was introduced as a model which might potentially provide good lower bounds for the ""off-diagonal"" Ramsey numbers R(3,k). In this model, edges of K_n are introduced one-by-one at random and added to the graph if they do not create a triangle; the resulting final (random) graph is denoted G_n,\triangle . In 2009, Bohman succeeded in following this process for a positive fra.
Notas:Description based upon print version of record.
Descripción Física:1 online resource (138 p.).
ISBN:9781470456566
1470456567

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