Geodesic
Hypergraph saturation irregularities
Natalie C. Behague1
1Queen Mary University of London
The electronic journal of combinatorics, Tome 25 (2018) no. 2
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Let $\mathcal{F}$ be a family of $r$-graphs. An $r$-graph $G$ is called $\mathcal{F}$-saturated if it does not contain any members of $\mathcal{F}$ but adding any edge creates a copy of some $r$-graph in $\mathcal{F}$. The saturation number $\operatorname{sat}(\mathcal{F},n)$ is the minimum number of edges in an $\mathcal{F}$-saturated graph on $n$ vertices. We prove that there exists a finite family $\mathcal{F}$ such that $\operatorname{sat}(\mathcal{F},n) / n^{r-1}$ does not tend to a limit. This settles a question of Pikhurko.
DOI : 10.37236/7727
Classification : 05C65, 05C35
Mots-clés : hypergraphs, saturation

Natalie C. Behague  1

1 Queen Mary University of London 
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Natalie C. Behague. Hypergraph saturation irregularities. The electronic journal of combinatorics, Tome 25 (2018) no. 2. doi: 10.37236/7727

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