Note on Gy. Elekes's conjectures concerning unavoidable patterns in proper colorings
Summary: A counterexample is presented to Gy. Elekes's conjecture concerning the existence of long \(2\)-colored paths in properly colored graphs. A modified version of the conjecture is given and its connections to a problem of Erdős-Gyárfás and to Szemerédi's theorem are examined.
scientific article; zbMATH DE number 1446391