Coverings by Few Monochromatic Pieces: A Transition Between Two Ramsey Problems

A. Gyárfás, Gábor N. Sárközy, Stanley Selkow

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The typical problem in (generalized) Ramsey theory is to find the order of the largest monochromatic member of a family (formula presented) (for example matchings, paths, cycles, connected subgraphs) that must be present in any edge coloring of a complete graph Kn with t colors. Another area is to find the minimum number of monochromatic members of (formula presented) that partition or cover the vertex set of every edge colored complete graph. Here we propose a problem that connects these areas: for a fixed positive integers s ≤ t, at least how many vertices can be covered by the vertices of no more than s monochromatic members of (formula presented) in every edge coloring of Kn with t colors. Several problems and conjectures are presented, among them a possible extension of a well-known result of Cockayne and Lorimer on monochromatic matchings for which we prove an initial step: every t-coloring of Kn contains a (t − 1)-colored matching of size k provided that (formula presented)

Original languageEnglish
JournalGraphs and Combinatorics
Volume31
Issue number1
DOIs
Publication statusPublished - 2015

Fingerprint

Coloring
Covering
Edge Coloring
Complete Graph
Color
Ramsey Theory
Edge-colored Graph
Colouring
Subgraph
Partition
Cover
Cycle
Path
Integer
Vertex of a graph

Keywords

  • Matchings
  • Monochromatic coverings
  • Ramsey problems

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Coverings by Few Monochromatic Pieces : A Transition Between Two Ramsey Problems. / Gyárfás, A.; Sárközy, Gábor N.; Selkow, Stanley.

In: Graphs and Combinatorics, Vol. 31, No. 1, 2015.

Research output: Contribution to journalArticle

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