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A01=Gonzalo Fiz Pontiveros
A01=Robert Morris
A01=Simon Griffiths
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Author_Gonzalo Fiz Pontiveros
Author_Robert Morris
Author_Simon Griffiths
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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 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. See more
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A01=Gonzalo Fiz PontiverosA01=Robert MorrisA01=Simon GriffithsAge Group_UncategorizedAuthor_Gonzalo Fiz PontiverosAuthor_Robert MorrisAuthor_Simon Griffithsautomatic-updateCategory1=Non-FictionCategory=PBDCategory=PBTCategory=PBVCOP=United StatesDelivery_Delivery within 10-20 working daysLanguage_EnglishPA=AvailablePrice_€50 to €100PS=Activesoftlaunch
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Product Details
  • Weight: 254g
  • Dimensions: 178 x 254mm
  • Publication Date: 30 Apr 2020
  • Publisher: American Mathematical Society
  • Publication City/Country: United States
  • Language: English
  • ISBN13: 9781470440718

About Gonzalo Fiz PontiverosRobert MorrisSimon Griffiths

Gonzalo Fiz Pontiveros Instituto Nacional de Matematica Pura e Aplicada (IMPA) Rio de Janeiro BrasilSimon Griffiths Instituto Nacional de Matematica Pura e Aplicada (IMPA) Rio de Janeiro BrasilRobert Morris Instituto Nacional de Matematica Pura e Aplicada (IMPA) Rio de Janeiro Brasil

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