In this paper, we study the rainbow Erdős-Rothschild problem with respect to 3-term arithmetic progressions. We obtain the asymptotic number of $r$-colorings of $[n]$ without rainbow 3-term arithmetic progressions, and we show that the typical colorings with this property are 2-colorings. We also prove that $[n]$ attains the maximum number of rainbow 3-term arithmetic progression-free $r$-colorings among all subsets of $[n]$. Moreover, the exact number of rainbow 3-term arithmetic progression-free $r$-colorings of $\mathbb{Z}_p$ is obtained, where $p$ is any prime and $\mathbb{Z}_p$ is the cyclic group of order $p$.
@article{10_37236_10249,
author = {Xihe Li and Hajo Broersma and Ligong Wang},
title = {Integer colorings with no rainbow 3-term arithmetic progression},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {2},
doi = {10.37236/10249},
zbl = {1495.11019},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10249/}
}
TY - JOUR
AU - Xihe Li
AU - Hajo Broersma
AU - Ligong Wang
TI - Integer colorings with no rainbow 3-term arithmetic progression
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/10249/
DO - 10.37236/10249
ID - 10_37236_10249
ER -
%0 Journal Article
%A Xihe Li
%A Hajo Broersma
%A Ligong Wang
%T Integer colorings with no rainbow 3-term arithmetic progression
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/10249/
%R 10.37236/10249
%F 10_37236_10249
Xihe Li; Hajo Broersma; Ligong Wang. Integer colorings with no rainbow 3-term arithmetic progression. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/10249
