Monochromatic path and cycle partitions in hypergraphs

András Gyárfás, Gábor N. Sárközy

Research output: Contribution to journalArticle

11 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
DOIs
Publication statusPublished - Jan 21 2013

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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