Description

Book Synopsis
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.

Table of Contents
  • Introduction
  • An overview of the proof
  • Martingale bounds: the line of peril and the line of death
  • Tracking everything else
  • Tracking $Y_e$, and mixing in the $Y$-graph
  • Whirlpools and Lyapunov functions
  • Independent sets and maximum degrees in $G_n,\triangle $
  • Bibliography.

The TriangleFree Process and the Ramsey Number

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    RRP £76.00 – you save £3.80 (5%)

    Order before 4pm today for delivery by Fri 19 Jun 2026.

    A Paperback by Gonzalo Fiz Pontiveros, Simon Griffiths, Robert Morris

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      View other formats and editions of The TriangleFree Process and the Ramsey Number by Gonzalo Fiz Pontiveros

      Publisher: MP-AMM American Mathematical
      Publication Date: 4/30/2020 12:00:00 AM
      ISBN13: 9781470440718, 978-1470440718
      ISBN10: 1470440717

      Description

      Book Synopsis
      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.

      Table of Contents
      • Introduction
      • An overview of the proof
      • Martingale bounds: the line of peril and the line of death
      • Tracking everything else
      • Tracking $Y_e$, and mixing in the $Y$-graph
      • Whirlpools and Lyapunov functions
      • Independent sets and maximum degrees in $G_n,\triangle $
      • Bibliography.

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