Alexandr Kostochka

you filter out the bad luck of a missing edge to reveal the massive, highly connected macrostructure that the raw density has forced into existence.

Kostochka's theorem, detailed in section 7.2, provides the exact mathematical threshold for this inevitability.

And Kostochka's bound is very specific.

He proves that to force a kr-minor, the average degree of the graph must scale relative to r square root log r.

Why that specific logarithmic function?