The extremal K4K_4K4-free graph conjecture for fractional separation dimension
The extremal K4K_4K4-free graph conjecture. For n≥10n\ge 10n≥10, the nnn-vertex graph not containing K4K_4K4 that maximizes πf\pi_fπf is K1,⌊(n−1)/2⌋,⌈(n−1)/2⌉K_{1,\lfloor (n-1)/2\rfloor,\lceil (n-1)/2\rceil}K1,⌊(n−1)/2⌋,⌈(n−1)/2⌉. Th…