A balanced edge-coloring of the complete graph is an edge-coloring such that every vertex is incident to each color the same number of times. In this short note, we present a construction of a balanced edge-coloring with six colors of the complete graph on $n=13^k$ vertices, for every positive integer $k$, with no rainbow $K_4$. This solves a problem by Erdős and Tuza.
@article{10_37236_11965,
author = {Felix Clemen and Adam Zsolt Wagner},
title = {Balanced edge-colorings avoiding rainbow cliques of size four},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {3},
doi = {10.37236/11965},
zbl = {1527.05062},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11965/}
}
TY - JOUR
AU - Felix Clemen
AU - Adam Zsolt Wagner
TI - Balanced edge-colorings avoiding rainbow cliques of size four
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/11965/
DO - 10.37236/11965
ID - 10_37236_11965
ER -
%0 Journal Article
%A Felix Clemen
%A Adam Zsolt Wagner
%T Balanced edge-colorings avoiding rainbow cliques of size four
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/11965/
%R 10.37236/11965
%F 10_37236_11965
Felix Clemen; Adam Zsolt Wagner. Balanced edge-colorings avoiding rainbow cliques of size four. The electronic journal of combinatorics, Tome 30 (2023) no. 3. doi: 10.37236/11965
