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- W3082187648 abstract "An edge-colored graph $F$ is {it rainbow} if each edge of $F$ has a unique color. The {it rainbow Turan number} $mathrm{ex}^*(n,F)$ of a graph $F$ is the maximum possible number of edges in a properly edge-colored $n$-vertex graph with no rainbow copy of $F$. The study of rainbow Turan numbers was introduced by Keevash, Mubayi, Sudakov, and Verstraete. Johnson and Rombach introduced the following rainbow-version of generalized Turan problems: for fixed graphs $H$ and $F$, let $mathrm{ex}^*(n,H,F)$ denote the maximum number of rainbow copies of $H$ in an $n$-vertex properly edge-colored graph with no rainbow copy of $F$. In this paper we investigate the case $mathrm{ex}^*(n,C_ell,P_ell)$ and give a general upper bound as well as exact results for $ell = 3,4,5$. Along the way we establish a new best upper bound on $mathrm{ex}^*(n,P_5)$. Our main motivation comes from an attempt to improve bounds on $mathrm{ex}^*(n,P_ell)$, which has been the subject of several recent manuscripts." @default.
- W3082187648 created "2020-09-08" @default.
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- W3082187648 date "2020-08-31" @default.
- W3082187648 modified "2023-09-27" @default.
- W3082187648 title "Rainbow cycles vs. rainbow paths" @default.
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