### Abstract

Here we address the problem to partition edge colored hypergraphs by mono- chromatic 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 into monochromatic loose cycles such that their number depends only on r and k.

Original language | English |
---|---|

Journal | Electronic Journal of Combinatorics |

Volume | 20 |

Issue number | 1 |

Publication status | Published - Jan 21 2013 |

### Fingerprint

### ASJC Scopus subject areas

- Geometry and Topology
- Theoretical Computer Science
- Computational Theory and Mathematics

### Cite this

*Electronic Journal of Combinatorics*,

*20*(1).

**Monochromatic path and cycle partitions in hypergraphs.** / Gyárfás, A.; Sárközy, Gábor N.

Research output: Contribution to journal › Article

*Electronic Journal of Combinatorics*, vol. 20, no. 1.

}

TY - JOUR

T1 - Monochromatic path and cycle partitions in hypergraphs

AU - Gyárfás, A.

AU - Sárközy, Gábor N.

PY - 2013/1/21

Y1 - 2013/1/21

N2 - Here we address the problem to partition edge colored hypergraphs by mono- chromatic 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 into monochromatic loose cycles such that their number depends only on r and k.

AB - Here we address the problem to partition edge colored hypergraphs by mono- chromatic 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 into monochromatic loose cycles such that their number depends only on r and k.

UR - http://www.scopus.com/inward/record.url?scp=84873348917&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84873348917&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84873348917

VL - 20

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

SN - 1077-8926

IS - 1

ER -