Polychromatic 4-coloring of guillotine subdivisions

Authors:
Elad Horev;Matthew J. Katz;Roi Krakovski;Maarten Löffler
Affiliations:
Department of Computer Science, Ben-Gurion University, Israel;Department of Computer Science, Ben-Gurion University, Israel;Department of Computer Science, Ben-Gurion University, Israel;Department of Information and Computing Sciences, Utrecht University, The Netherlands
Venue:
Information Processing Letters
Year:
2009

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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.