### Abstract

A (D, c)-coloring of the complete graph K^{n} is a coloring of the edges with c colors such that all monochromatic connected subgraphs have at most D vertices. Resolvable block designs with c parallel classes and with block size D are natural examples of (D, c)-colorings. However, (D, c)-colorings are more relaxed structures. We investigate the largest n such that K^{n} has a (D, c)-coloring. Our main tool is the fractional matching theory of hypergraphs.

Original language | English |
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Pages (from-to) | 217-226 |

Number of pages | 10 |

Journal | Annals of Discrete Mathematics |

Volume | 43 |

Issue number | C |

DOIs | |

Publication status | Published - 1989 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

**Covering the Complete Graph by Partitions.** / Füredi, Z.

Research output: Contribution to journal › Article

*Annals of Discrete Mathematics*, vol. 43, no. C, pp. 217-226. https://doi.org/10.1016/S0167-5060(08)70576-4

}

TY - JOUR

T1 - Covering the Complete Graph by Partitions

AU - Füredi, Z.

PY - 1989

Y1 - 1989

N2 - A (D, c)-coloring of the complete graph Kn is a coloring of the edges with c colors such that all monochromatic connected subgraphs have at most D vertices. Resolvable block designs with c parallel classes and with block size D are natural examples of (D, c)-colorings. However, (D, c)-colorings are more relaxed structures. We investigate the largest n such that Kn has a (D, c)-coloring. Our main tool is the fractional matching theory of hypergraphs.

AB - A (D, c)-coloring of the complete graph Kn is a coloring of the edges with c colors such that all monochromatic connected subgraphs have at most D vertices. Resolvable block designs with c parallel classes and with block size D are natural examples of (D, c)-colorings. However, (D, c)-colorings are more relaxed structures. We investigate the largest n such that Kn has a (D, c)-coloring. Our main tool is the fractional matching theory of hypergraphs.

UR - http://www.scopus.com/inward/record.url?scp=77957044132&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957044132&partnerID=8YFLogxK

U2 - 10.1016/S0167-5060(08)70576-4

DO - 10.1016/S0167-5060(08)70576-4

M3 - Article

AN - SCOPUS:77957044132

VL - 43

SP - 217

EP - 226

JO - Annals of Discrete Mathematics

JF - Annals of Discrete Mathematics

SN - 0167-5060

IS - C

ER -