Diameter-bounded blow-up conjecture for generalized Turán numbers
Diameter-bounded blow-up conjecture for generalized Turán numbers
Let be a graph with diameter at most and chromatic number . Diameter-bounded blow-up conjecture. The generalized Turán number is asymptotically achieved by a blow-up of . 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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