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arXiv · 2301.10393

On the rainbow planar Tur\'an number of paths

Ervin Győri·Ryan R. Martin·Addisu Paulos·Casey Tompkins·Kitti Varga
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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 edges among $n$-vertex properly edge-colored graphs not containing a rainbow-$F$, known as the rainbow Tur\'an problem, was initiated by Keevash, Mubayi, Sudakov and Verstra\"ete. We investigate a variation of this problem with the additional restriction that the graph is planar, and we denote the corresponding extremal number by $\ex_{\p}^*(n,F)$. In particular, we determine $\ex_{\p}^*(n,P_5)$, where $P_5$ denotes the $5$-vertex path.

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Ervin Győri, Ryan R. Martin, Addisu Paulos, Casey Tompkins, Kitti Varga. 2023-01-25. On the rainbow planar Tur\'an number of paths. https://arxiv.org/abs/2301.10393

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