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Is minimum colors needed to assign colors to edges of complete graph $K_n$ so that every $2t$ simple cycle where $t\in\Big\{1,\dots,2\Big\lfloor\frac{n}2\Big\rfloor\Big\}$ contains atleast $t+1$ ...

The following question arised as a side-question in a geometric problem. It has a "feel" similar to problems in Ramsey-theory, but I have not found any mention of it (also I'm not very familiar with ...