### Abstract

We conjecture that for n > 4 (k - 1) every 2-coloring of the edges of the complete graph K_{n} 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 K_{n} contains a k-connected monochromatic subgraph with at least n - 12 k vertices.

Original language | English |
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Pages (from-to) | 1722-1725 |

Number of pages | 4 |

Journal | Discrete Mathematics |

Volume | 308 |

Issue number | 9 |

DOIs | |

Publication status | Published - 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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## Cite this

Bollobás, B., & Gyárfás, A. (2008). Highly connected monochromatic subgraphs.

*Discrete Mathematics*,*308*(9), 1722-1725. https://doi.org/10.1016/j.disc.2006.01.030