Dense subgraphs in the H-free process

@article{Warnke2011DenseSI,
  title={Dense subgraphs in the H-free process},
  author={Lutz Warnke},
  journal={Discret. Math.},
  year={2011},
  volume={311},
  pages={2703-2707}
}
  • L. Warnke
  • Published 1 March 2010
  • Mathematics
  • Discret. Math.
The Reverse H‐free Process for Strictly 2‐Balanced Graphs
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The diamond‐free process
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When does the K4‐free process stop?
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  • Mathematics
    Random Struct. Algorithms
  • 2014
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C O ] 1 7 A pr 2 01 2 When does the K 4-free process stop ?
  • 2012
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  • L. Warnke
  • Mathematics
    Random Struct. Algorithms
  • 2014
TLDR
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J an 2 01 1 The C l-free process
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The Final Size of the Cℓ-free Process
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The Final Size of the Cℓ-free Process
TLDR
The differential equation method is used and it is shown that the final graph produced by this random graph process has maximum degree $O( (n \log n)^{1/(\ell-1)})$ and, consequently, size $O (n^{\ell/(\ll-1)}(\log n).
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The H-free process, for some fixed graph H, is the random graph process defined by starting with an empty graph on n vertices and then adding edges one at a time, chosen uniformly at random subject
Random maximal H-free graphs
Given a graph H, a random maximal H-free graph is constructed by the following random greedy process. First assign to each edge of the complete graph on n vertices a birthtime which is uniformly
No Dense Subgraphs Appear in the Triangle-free Graph Process
TLDR
It is shown that there exists a constant $c$ such that asymptotically almost surely no copy of any fixed finite triangle-free graph on $k$ vertices with at least $ck$ edges appears in the triangle- free graph process.
The K_4-free process
We consider the K_4-free process. In this process, the edges of the complete n-vertex graph are traversed in a uniformly random order, and each traversed edge is added to an initially empty evolving
The Final Size of the C4-Free Process
We consider the following random graph process: starting with n isolated vertices, add edges uniformly at random provided no such edge creates a copy of C4. We show that, with probability tending to
4-cycles at the Triangle-free Process
On the Size of a Random Maximal Graph
TLDR
A variety of techniques are used to show that the size of the random maximal bipartite graph is quadratic in n but of order only n3'2 in the triangle—free case and a slight improvement in the lower bound of the Ramsey number r(3, t).
The triangle-free process
The random planar graph process
TLDR
The following variant of the classical random graph process introduced by Erdős and Rényi is considered, showing that for all ε > 0, with high probability, θ(n) edges have to be tested before the number of edges in the graph reaches (1 + ε)n.
Triangle‐free subgraphs in the triangle‐free process
Consider the triangle‐free process, which is defined as follows. Start with G(0), an empty graph on n vertices. Given G(i ‐ 1), let G(i) = G(i ‐ 1) ∪{g(i)}, where g(i) is an edge that is chosen
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