Spectral generalized Tur\'an problems
Abstract
Combining two well-studied variants of the classical Tur\'an problem, the generalized Tur\'an problem and the spectral Tur\'an problem, we introduce the spectral generalized Tur\'an problem and establish a general theorem that extends the result of Keevash--Lenz--Mubayi~KLM14 on the spectral Tur\'an problem in this broader setting. As a quick application, we obtain the spectral Erdos Pentagon Theorem. We also introduce the notion of entropic density for generalized Tur\'an problems, and show that it coincides with the generalized spectral radius, extending a recent result of Chao--Hans on entropic Tur\'an density.
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