Let $F$ be a fixed graph. The rainbow Turán number of $F$ is defined as the maximum number of edges in a graph on $n$ vertices that has a proper edge-coloring with no rainbow copy of $F$ (i.e., a copy of $F$ all of whose edges have different colours). The systematic study of such problems was initiated by Keevash, Mubayi, Sudakov and Verstraëte. In this paper, we show that the rainbow Turán number of a path with $k+1$ edges is less than $\left(9k/7+2\right) n$, improving an earlier estimate of Johnston, Palmer and Sarkar.
1
Central European University
2
Central European University and Alfréd Rényi Institute of Mathematics
3
École Polytechnique Fédérale de Lausanne
Beka Ergemlidze; Ervin Győri; Abhishek Methuku. On the rainbow Turán number of paths. The electronic journal of combinatorics, Tome 26 (2019) no. 1. doi: 10.37236/7889
@article{10_37236_7889,
author = {Beka Ergemlidze and Ervin Gy\H{o}ri and Abhishek Methuku},
title = {On the rainbow {Tur\'an} number of paths},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {1},
doi = {10.37236/7889},
zbl = {1406.05045},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7889/}
}
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AU - Abhishek Methuku
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