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arXiv · 1002.2316

No Dense Subgraphs Appear in the Triangle-free Graph Process

Stefanie Gerke·Tamás Makai
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Abstract

Consider the triangle-free graph process, which starts from the empty graph on $n$ vertices and a random ordering of the possible ${n \choose 2}$ edges; the edges are added in this ordering provided the graph remains triangle free. We will show that there exists a constant $c$ such that no copy of any fixed finite triangle-free graph on $k$ vertices with at least $ck$ edges asymptotically almost surely appears in the triangle-free graph process.

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BibTeXRIS

Stefanie Gerke, Tamás Makai. 2010-02-11. No Dense Subgraphs Appear in the Triangle-free Graph Process. https://arxiv.org/abs/1002.2316

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