Monochromatic path and cycle partitions in hypergraphs

A. Gyárfás, Gábor N. Sárközy

Research output: Contribution to journalArticle

10 Citations (Scopus)

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 languageEnglish
JournalElectronic Journal of Combinatorics
Volume20
Issue number1
Publication statusPublished - Jan 21 2013

Fingerprint

Coloring
Hypergraph
Uniform Hypergraph
Partition
Color
Cycle
Path
Colouring
Distinct
Graph in graph theory
Vertex of a graph

ASJC Scopus subject areas

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

Cite this

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

In: Electronic Journal of Combinatorics, Vol. 20, No. 1, 21.01.2013.

Research output: Contribution to journalArticle

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