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

Pontiveros, Gonzalo Fiz; Griffiths, Simon; Morris, Robert

 
9781470440718: The Triangle-Free Process and the Ramsey Number R (3,k)
Couverture souple
ISBN 10 : 1470440717 ISBN 13 : 9781470440718
Editeur : American Mathematical Society, 2020

Synopsis

The areas of Ramsey theory and random graphs have been closely linked ever since Erdos'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 fraction of its duration, and thus obtained a second proof of Kim's celebrated result that $R(3,k) = \Theta \big ( k^2 / \log k \big )$. In this paper the authors improve the results of both Bohman and Kim and follow the triangle-free process all the way to its asymptotic end.

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À propos de l?auteur

Gonzalo Fiz Pontiveros, Instituto Nacional de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, Brasil

Simon Griffiths, Instituto Nacional de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, Brasil

Robert Morris, Instituto Nacional de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, Brasil

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2020
Langue
anglais
ISBN 10 
1470440717
ISBN 13 
9781470440718
Reliure
Broché
Nombre de pages
125
Coordonnées du fabricant
non disponible
Personne responsable
non disponible