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arXiv · 1609.00069

Rainbow Tur\'an problems for paths and forests of stars

Daniel Johnston·Cory Palmer·Amites Sarkar
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Abstract

For a fixed graph $F$, we would like to determine the maximum number of edges in a properly edge-colored graph on $n$ vertices which does not contain a {\emph rainbow copy} of $F$, that is, a copy of $F$ all of whose edges receive a different color. This maximum, denoted by $ex^*(n,F)$, is the {\emph rainbow Tur\'an number} of $F$, and its systematic study was initiated by Keevash, Mubayi, Sudakov and Verstra\"ete in 2007. We determine $ex^*(n,F)$ exactly when $F$ is a forest of stars, and give bounds on $ex^*(n,F)$ when $F$ is a path with $k$ edges, disproving a conjecture in Keevash et al.

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Daniel Johnston, Cory Palmer, Amites Sarkar. 2016-08-31. Rainbow Tur\'an problems for paths and forests of stars. https://arxiv.org/abs/1609.00069

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