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arXiv · 2308.01564

Sparse pancyclic subgraphs of random graphs

Yahav Alon·Michael Krivelevich
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Abstract

It is known that the complete graph $K_n$ contains a pancyclic subgraph with $n+(1+o(1))\cdot \log _2 n$ edges, and that there is no pancyclic graph on $n$ vertices with fewer than $n+\log _2 (n-1) -1$ edges. We show that, with high probability, $G(n,p)$ contains a pancyclic subgraph with $n+(1+o(1))\log_2 n$ edges for $p \ge p^*$, where $p^*=(1+o(1))\ln n/n$, right above the threshold for pancyclicity.

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Yahav Alon, Michael Krivelevich. 2023-08-03. Sparse pancyclic subgraphs of random graphs. https://arxiv.org/abs/2308.01564

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