## Abstract

A polychromatic k-coloring of a plane graph G is an assignment of k colors to the vertices of G such that each face of G, except possibly for the outer face, has all k colors on its boundary. A rectangular partition is a partition of a rectangle R into a set of non-overlapping rectangles such that no four rectangles meet at a point. It was conjectured in [Y. Dinitz, M.J. Katz, R. Krakovski, Guarding rectangular partitions, in: 23rd European Workshop Computational Geometry, 2007, pp. 30-33] that every rectangular partition admits a polychromatic 4-coloring. In this note we prove the conjecture for guillotine subdivisions - a well-studied subfamily of rectangular partitions.

Original language | English |
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Pages (from-to) | 690-694 |

Number of pages | 5 |

Journal | Information Processing Letters |

Volume | 109 |

Issue number | 13 |

DOIs | |

State | Published - 15 Jun 2009 |

## Keywords

- Algorithms
- Combinatorial and computational geometry
- Guillotine subdivisions
- Polychromatic coloring

## ASJC Scopus subject areas

- Theoretical Computer Science
- Signal Processing
- Information Systems
- Computer Science Applications