### 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 |
---|---|

Pages (from-to) | 1722-1725 |

Number of pages | 4 |

Journal | Discrete Mathematics |

Volume | 308 |

Issue number | 9 |

DOIs | |

Publication status | Published - May 6 2008 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

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

**Highly connected monochromatic subgraphs.** / Bollobás, Béla; Gyárfás, A.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 308, no. 9, pp. 1722-1725. https://doi.org/10.1016/j.disc.2006.01.030

}

TY - JOUR

T1 - Highly connected monochromatic subgraphs

AU - Bollobás, Béla

AU - Gyárfás, A.

PY - 2008/5/6

Y1 - 2008/5/6

N2 - 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.

AB - 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.

KW - Edge coloring of complete graphs

KW - k-connected monochromatic subgraphs

UR - http://www.scopus.com/inward/record.url?scp=38949216750&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38949216750&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2006.01.030

DO - 10.1016/j.disc.2006.01.030

M3 - Article

VL - 308

SP - 1722

EP - 1725

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 9

ER -