Geodesic
No dense subgraphs appear in the triangle-free graph process
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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Consider the triangle-free graph process, which starts from the empty graph on $n$ vertices and in every step an edge is added that is chosen uniformly at random from all non-edges that do not form a triangle with the existing edges. We will show 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.
DOI : 10.37236/655
Classification : 05C80 
@article{10_37236_655,
     author = {Stefanie Gerke and Tam\'as Makai},
     title = {No dense subgraphs appear in the triangle-free graph process},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/655},
     zbl = {1229.05249},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/655/}
}
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Stefanie Gerke; Tamás Makai. No dense subgraphs appear in the triangle-free graph process. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/655

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