Partitioning 3-colored complete graphs into three monochromatic cycles

A. Gyárfás, Miklós Ruszinkó, Gábor N. Sárközy, E. Szemerédi

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

We show in this paper that in every 3-coloring of the edges of Kn all but o(n) of its vertices can be partitioned into three monochromatic cycles. From this, using our earlier results, actually it follows that we can partition all the vertices into at most 17 monochromatic cycles, improving the best known bounds. If the colors of the three monochromatic cycles must be different then one can cover (3/4 - o(1))n vertices and this is close to best possible.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalElectronic Journal of Combinatorics
Volume18
Issue number1
Publication statusPublished - 2011

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Colored Graph
Coloring
Complete Graph
Partitioning
Color
Cycle
Colouring
Partition
Cover

ASJC Scopus subject areas

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

Cite this

Partitioning 3-colored complete graphs into three monochromatic cycles. / Gyárfás, A.; Ruszinkó, Miklós; Sárközy, Gábor N.; Szemerédi, E.

In: Electronic Journal of Combinatorics, Vol. 18, No. 1, 2011, p. 1-16.

Research output: Contribution to journalArticle

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