Given a graph $H$, a perfect $H$-factor in a graph $G$ is a collection of vertex-disjoint copies of $H$ spanning $G$. Kühn and Osthus showed that the minimum degree threshold for a graph $G$ to contain a perfect $H$-factor is either given by $1-1/\chi(H)$ or by $1-1/\chi_{cr}(H)$ depending on certain natural divisibility considerations. Given a graph $G$ of order $n$, a $2$-edge-coloring of $G$ and a subgraph $G'$ of $G$, we say that $G'$ has high discrepancy if it contains significantly (linear in $n$) more edges of one color than the other. Balogh, Csaba, Pluhár and Treglown asked for the minimum degree threshold guaranteeing that every 2-edge-coloring of $G$ has an $H$-factor with high discrepancy and they settled the case where $H$ is a clique. Here we completely resolve this question by determining the minimum degree threshold for high discrepancy of $H$-factors for every graph $H$.
@article{10_37236_12145,
author = {Domagoj Brada\v{c} and Micha Christoph and Lior Gishboliner},
title = {Minimum degree threshold for {\(H\)-factors} with high discrepancy},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {3},
doi = {10.37236/12145},
zbl = {1548.05181},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12145/}
}
TY - JOUR
AU - Domagoj Bradač
AU - Micha Christoph
AU - Lior Gishboliner
TI - Minimum degree threshold for \(H\)-factors with high discrepancy
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/12145/
DO - 10.37236/12145
ID - 10_37236_12145
ER -
%0 Journal Article
%A Domagoj Bradač
%A Micha Christoph
%A Lior Gishboliner
%T Minimum degree threshold for \(H\)-factors with high discrepancy
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/12145/
%R 10.37236/12145
%F 10_37236_12145
Domagoj Bradač; Micha Christoph; Lior Gishboliner. Minimum degree threshold for \(H\)-factors with high discrepancy. The electronic journal of combinatorics, Tome 31 (2024) no. 3. doi: 10.37236/12145
