Gyárfas proved that every coloring of the edges of $K_n$ with $t+1$ colors contains a monochromatic connected component of size at least $n/t$. Later, Gyárfás and Sárközy asked for which values of $\gamma=\gamma(t)$ does the following strengthening for almost complete graphs hold: if $G$ is an $n$-vertex graph with minimum degree at least $(1-\gamma)n$, then every $(t+1)$-edge coloring of $G$ contains a monochromatic component of size at least $n/t$. We show $\gamma= 1/(6t^3)$ suffices, improving a result of DeBiasio, Krueger, and Sárközy.
@article{10_37236_9824,
author = {Zolt\'an F\"uredi and Ruth Luo},
title = {Large monochromatic components in almost complete graphs and bipartite graphs},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {2},
doi = {10.37236/9824},
zbl = {1466.05067},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9824/}
}
TY - JOUR
AU - Zoltán Füredi
AU - Ruth Luo
TI - Large monochromatic components in almost complete graphs and bipartite graphs
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/9824/
DO - 10.37236/9824
ID - 10_37236_9824
ER -
%0 Journal Article
%A Zoltán Füredi
%A Ruth Luo
%T Large monochromatic components in almost complete graphs and bipartite graphs
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/9824/
%R 10.37236/9824
%F 10_37236_9824
Zoltán Füredi; Ruth Luo. Large monochromatic components in almost complete graphs and bipartite graphs. The electronic journal of combinatorics, Tome 28 (2021) no. 2. doi: 10.37236/9824
