On the rainbow planar Turán number of paths

Győri, Ervin and Martin, Ryan R. and Paulos, Addisu and Tompkins, Casey and Varga, Kitti Katalin (2025) On the rainbow planar Turán number of paths. DISCRETE MATHEMATICS, 348 (10). ISSN 0012-365X

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Abstract

An edge-colored graph is said to contain a rainbow-F if it contains F as a subgraph and every edge of F is a distinct color. The problem of maximizing the number of edges among n-vertex properly edge-colored graphs not containing a rainbow-F, known as the rainbow Turán problem, was initiated by Keevash, Mubayi, Sudakov, and Verstraëte. We investigate a variation of this problem with the additional restriction that the graph is planar and we denote the corresponding extremal number by exP⁎(n,F). In particular, we determine exP⁎(n,P5), where P5 denotes the 5-vertex path. © 2025

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