No Dense Subgraphs Appear in the Triangle-free Graph Process

Stefanie Gerke, Tamás Makai

Abstract


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.


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