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Status: Unchecked ×Keyword: edge addition ×Clear all

2 claims from 1 paper

1. Mathematics › Limits and Structures in Graph Theory

   The triangle-free process

   Bohman · arXiv (Cornell University) · 2008

   The paper analyses a random process that adds edges without making triangles, finds the likely order of magnitude of the final edge count, and uses it to reprove a bound on R(3,t) and slightly improve R(4,t).

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   1. UncheckedThe triangle-free random graph process is very likely to yield a Ramsey R(3,t) graph, giving a new proof of Kim's lower bound on R(3,t).“As a corollary we show that the triangle-free process is very likely to produce a Ramsey R(3,t) graph; that is, our analysis of the triangle-free process gives a new proof of the lower bound on R(3,t) previously established by Jeong Han Kim.”
   2. UncheckedMethods from analysing the triangle-free process also apply to the K_4-free process, slightly improving the best known lower bound on R(4,t).“The techniques introduced extend to the K_4-free process thereby establishing a small improvement in the best known lower bound on the Ramsey number R(4,t).”