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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Order before 4pm today for delivery by Mon 19 Jan 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
    Also in:
    Combinatorics and graph theory Discrete mathematics

    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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