Tootfinder

🇺🇦 #NowPlaying on BBCRadio3's #SundayMorning
Henry Purcell, Anonymous, The King's Consort, Gillian Fisher, Michael George, Nigel Short, Rogers Covey‐Crump, Evelyn Tubb, Charles Pott & James Bowman:
🎵 Welcome, Welcome, Glorious Morn, Z 338 (1st mvt, 'Symphony')
#Anonymous
Please 🔁 BOOST to share what you like
- your followers don't see if you ⭐ favourite a post

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

On saturation numbers of complete multipartite graphs and even cycles
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.