TY - JOUR

T1 - Polychromatic 4-coloring of guillotine subdivisions

AU - Horev, Elad

AU - Katz, Matthew J.

AU - Krakovski, Roi

AU - Löffler, Maarten

PY - 2009/6/15

Y1 - 2009/6/15

N2 - 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.

AB - 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.

KW - Algorithms

KW - Combinatorial and computational geometry

KW - Guillotine subdivisions

KW - Polychromatic coloring

UR - http://www.scopus.com/inward/record.url?scp=67349114200&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2009.03.006

DO - 10.1016/j.ipl.2009.03.006

M3 - Article

AN - SCOPUS:67349114200

VL - 109

SP - 690

EP - 694

JO - Information Processing Letters

JF - Information Processing Letters

SN - 0020-0190

IS - 13

ER -