### 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 |
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Pages (from-to) | 95-106 |

Number of pages | 12 |

Journal | Graphs and Combinatorics |

Volume | 5 |

Issue number | 1 |

DOIs | |

Publication status | Published - Dec 1989 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Mathematics(all)

### Cite this

*Graphs and Combinatorics*,

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

**Legitimate colorings of projective planes.** / Alon, N.; Füredi, Z.

Research output: Contribution to journal › Article

*Graphs and Combinatorics*, vol. 5, no. 1, pp. 95-106. https://doi.org/10.1007/BF01788662

}

TY - JOUR

T1 - Legitimate colorings of projective planes

AU - Alon, N.

AU - Füredi, Z.

PY - 1989/12

Y1 - 1989/12

N2 - For a projective plane ℙn of order n, let κ{script}(ℙn) denote the minimum number k, so that there is a coloring of the points of ℙn 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}(ℙn) ≤ 8 for every projective plane ℙn of order n.

AB - For a projective plane ℙn of order n, let κ{script}(ℙn) denote the minimum number k, so that there is a coloring of the points of ℙn 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}(ℙn) ≤ 8 for every projective plane ℙn of order n.

UR - http://www.scopus.com/inward/record.url?scp=0040701229&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040701229&partnerID=8YFLogxK

U2 - 10.1007/BF01788662

DO - 10.1007/BF01788662

M3 - Article

AN - SCOPUS:0040701229

VL - 5

SP - 95

EP - 106

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

SN - 0911-0119

IS - 1

ER -