Highly connected monochromatic subgraphs

Béla Bollobás, András Gyárfás

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

We conjecture that for n > 4 (k - 1) every 2-coloring of the edges of the complete graph Kn contains a k-connected monochromatic subgraph with at least n - 2 (k - 1) vertices. This conjecture, if true, is best possible. Here we prove it for k = 2, and show how to reduce it to the case n < 7 k - 6. We prove the following result as well: for n > 16 k every 2-colored Kn contains a k-connected monochromatic subgraph with at least n - 12 k vertices.

Original languageEnglish
Pages (from-to)1722-1725
Number of pages4
JournalDiscrete Mathematics
Volume308
Issue number9
DOIs
Publication statusPublished - May 6 2008

Keywords

  • Edge coloring of complete graphs
  • k-connected monochromatic subgraphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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