Claims

../

2008_03_09_fomin_villanger: Theorem 1 of Fomin and Villanger proves that an n-vertex graph has O(1.6181^n) minimal separators, so the limit is at most the golden ratio; accepted on the refereed paper in Combinatorica 32 (2012).

2008_07_02_fomin_kratsch_todinca_villanger: Fomin, Kratsch, Todinca and Villanger prove that an n-vertex graph has O(1.7087^n) minimal separators, the first proof that the limit is below 2; accepted on the refereed paper in SIAM J. Comput. 38 (2008).

2015_03_04_gaspers_mackenzie: Theorem 1 of Gaspers and Mackenzie proves by a short measure argument that an n-vertex graph has O(rho^n n) minimal separators, rho the golden ratio; accepted on the refereed paper in J. Graph Theory 87 (2018).

2024_09_04_bradac: Bradač's note proves that the n-th root of the maximum number of minimal cuts converges to a limit at most 2 to the binary entropy of one third, below 1.8899; refereed in J. Graph Theory 108 (2025), credited by the site.

---