### Abstract

An (r,n)-split coloring of a complete graph is an edge coloring with r colors under which the vertex set is partitionable into r parts so that for each i, part i does not contain K_{n} in color i. This generalizes the notion of split graphs which correspond to (2, 2)-split colorings. The smallest N for which the complete graph K_{N} has a coloring which is not (r,n)-split is denoted by f_{r}(n). Balanced (r,n)-colorings are defined as edge r-colorings of K_{N} such that every subset of ⌈N/r⌉ vertices contains a monochromatic K_{n} in all colors. Then g_{r}(n) is defined as the smallest N such that K_{N} has a balanced (r,n)-coloring. The definitions imply that f_{r}(n)≤g,(n). The paper gives estimates and exact values of these functions for various choices of parameters.

Original language | English |
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Pages (from-to) | 79-86 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 200 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Apr 6 1999 |

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### Keywords

- Balanced coloring
- Split graphs
- Vertex set

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics