Ramsey theory constructions from hypergraph matchings (Q6621271)

In this paper, the authors use results about conflict-free hypergraph matchings to give asymptotically optimal constructions in generalized Ramsey theory. For example, the authors present an edge-coloring of \(K_{n,n}\) with \(2n/3+o(n)\) colors such that each 4-cycle receives at least three colors on its edges. This answers a question of \textit{M. Axenovich} et al. [J. Comb. Theory, Ser. B 79, No. 1, 66--86 (2000; Zbl 1023.05101)]. Also, the authors exhibit an edge-coloring of \(K_n\) with \(5n/6 + o(n)\) colors that assigns each copy of \(K_4\) at least five colors. This gives an alternative short solution to an old question of \textit{P. Erdős} and \textit{A. Gyárfás} [Combinatorica 17, No. 4, 459--467 (1997; Zbl 0910.05034)] that was recently answered by \textit{P. Bennett} et al. [J. Comb. Theory, Ser. B 169, 253--297 (2024; Zbl 1548.05109)].