Papers › Inverting the Turán Problem
Inverting the Turán Problem
Joseph Briggs, Christopher Cox
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Classical questions in extremal graph theory concern the asymptotics of ex(G, ℋ) where ℋ is a fixed family of graphs and G=Gₙ is taken from a `standard' increasing sequence of host graphs (G₁, G₂, …), most often Kₙ or K_(n,n). Inverting the question, we can instead ask how large e(G) can be with respect to ex(G,ℋ). We show that the standard sequences indeed maximize e(G) for some choices of ℋ, but not for others. Many interesting questions and previous results arise very naturally in this context, which also, unusually, gives rise to sensible extremal questions concerning multigraphs and non-uniform hypergraphs.
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