Author:
Babiński Sebastian,Grzesik Andrzej
Abstract
In 1959 Erd\H os and Gallai proved the asymptotically optimal bound for the maximum number of edges in graphs not containing a path of a fixed length. We investigate a rainbow version of the theorem, in which one considers $k \geq 1$ graphs on a common set of vertices not creating a path having edges from different graphs and asks for the maximum number of edges in each graph. We prove the asymptotically optimal bound in the case of a path on three edges and any $k \geq 1$.
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1. Directed graphs without rainbow triangles;Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications;2023