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arXiv · 2506.09767

On saturation numbers of complete multipartite graphs and even cycles

Ali Mohammadian·Milad Poursoltani·Behruz Tayfeh-Rezaie
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Abstract

Given positive integer $n$ and graph $F$, the saturation number $\mathrm{sat}(n, F)$ is the minimum number of edges in an edge-maximal $F$-free graph on $n$ vertices. In this paper, we determine asymptotic behavior of $\mathrm{sat}(n, F)$ when $F$ is either a complete multipartite graph or a cycle graph whose length is even and large enough. This extends a result by Bohman, Fonoberova, and Pikhurko from 2010 as well as partially resolves a conjecture of Füredi and Kim from 2013.

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Ali Mohammadian, Milad Poursoltani, Behruz Tayfeh-Rezaie. 2025-06-11. On saturation numbers of complete multipartite graphs and even cycles. https://arxiv.org/abs/2506.09767

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