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arXiv · 2212.06101

Tight concentration of star saturation number in random graphs

Sergej Demyanov·Maksim Zhukovskii
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Abstract

For given graphs $F$ and $G$, the minimum number of edges in an inclusion-maximal $F$-free subgraph of $G$ is called the $F$-saturation number and denoted $\mathrm{sat}(G, F)$. For the star $F=K_{1,r}$, the asymptotics of $\mathrm{sat}(G(n,p),F)$ is known. We prove a sharper result: whp $\mathrm{sat}(G(n,p), K_{1,r})$ is concentrated in a set of 2 consecutive points.

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Sergej Demyanov, Maksim Zhukovskii. 2022-12-12. Tight concentration of star saturation number in random graphs. https://arxiv.org/abs/2212.06101

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