Here we address the problem to partition edge colored hypergraphs by monochromatic paths and cycles generalizing a well-known similar problem for graphs.We show that $r$-colored $r$-uniform complete hypergraphs can be partitioned into monochromatic Berge-paths of distinct colors. Also, apart from $2k-5$ vertices, $2$-colored $k$-uniform hypergraphs can be partitioned into two monochromatic loose paths.In general, we prove that in any $r$-coloring of a $k$-uniform hypergraph there is a partition of the vertex set intomonochromatic loose cycles such that their number depends only on $r$ and $k$.
@article{10_37236_2631,
author = {Andr\'as Gy\'arf\'as and G\'abor N. S\'ark\"ozy},
title = {Monochromatic path and cycle partitions in hypergraphs},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {1},
doi = {10.37236/2631},
zbl = {1266.05091},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2631/}
}
TY - JOUR
AU - András Gyárfás
AU - Gábor N. Sárközy
TI - Monochromatic path and cycle partitions in hypergraphs
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/2631/
DO - 10.37236/2631
ID - 10_37236_2631
ER -
%0 Journal Article
%A András Gyárfás
%A Gábor N. Sárközy
%T Monochromatic path and cycle partitions in hypergraphs
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/2631/
%R 10.37236/2631
%F 10_37236_2631
András Gyárfás; Gábor N. Sárközy. Monochromatic path and cycle partitions in hypergraphs. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2631
