Diameter-bounded blow-up conjecture for generalized Turán numbers

Let GG be a graph with diameter at most 2r22r-2 and chromatic number χ(G)<r\chi(G)<r. Diameter-bounded blow-up conjecture. The generalized Turán number ex(n,G,Kr)\operatorname{ex}(n,G,K_r) is asymptotically achieved by a blow-up of Kr1K_{r-1}. This is proposed as a replacement for the refuted Lidický–Murphy conjecture: bounding the diameter is intended to exclude the obstruction used in the counterexample. The provided text does not state whether this problem has been resolved, so its status remains open.

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Primary source

Andrzej Grzesik, Ervin Győri, Nika Salia and Casey Tompkins, “Subgraph densities in K_r-free graphs”, arXiv:2205.13455 (2022).

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