In this paper we study the monochromatic loose-cycle partition problem for non-complete hypergraphs. Our main result is that in any $r$-coloring of a $k$-uniform hypergraph with independence number $\alpha$ there is a partition of the vertex set into monochromatic loose cycles such that their number depends only on $r$, $k$ and $\alpha$. We also give an extension of the following result of Pósa to hypergraphs: the vertex set of every graph $G$ can be partitioned into at most $\alpha(G)$ cycles, edges and vertices.
@article{10_37236_4062,
author = {Andr\'as Gy\'arf\'as and G\'abor S\'ark\"ozy},
title = {Monochromatic loose-cycle partitions in hypergraphs},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {2},
doi = {10.37236/4062},
zbl = {1300.05199},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4062/}
}
TY - JOUR
AU - András Gyárfás
AU - Gábor Sárközy
TI - Monochromatic loose-cycle partitions in hypergraphs
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/4062/
DO - 10.37236/4062
ID - 10_37236_4062
ER -
%0 Journal Article
%A András Gyárfás
%A Gábor Sárközy
%T Monochromatic loose-cycle partitions in hypergraphs
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/4062/
%R 10.37236/4062
%F 10_37236_4062
András Gyárfás; Gábor Sárközy. Monochromatic loose-cycle partitions in hypergraphs. The electronic journal of combinatorics, Tome 21 (2014) no. 2. doi: 10.37236/4062
