### Abstract

For a projective plane ℙ_{n} of order n, let κ{script}(ℙ_{n}) denote the minimum number k, so that there is a coloring of the points of ℙ_{n} in k colors such that no two distinct lines contain precisely the same number of points of each color. Answering a question of A. Rosa, we show that for all sufficiently large n, 5 ≤κ{script}(ℙ_{n}) ≤ 8 for every projective plane ℙ_{n} of order n.

Original language | English (US) |
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Pages (from-to) | 95-106 |

Number of pages | 12 |

Journal | Graphs and Combinatorics |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1989 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

## Fingerprint Dive into the research topics of 'Legitimate colorings of projective planes'. Together they form a unique fingerprint.

## Cite this

Alon, N., & Füredi, Z. (1989). Legitimate colorings of projective planes.

*Graphs and Combinatorics*,*5*(1), 95-106. https://doi.org/10.1007/BF01788662