Non-Monochromatic and Conflict-Free Colorings on Tree Spaces and Planar Network Spaces

Abstract

It is well known that any set of n intervals in R 1 admits a non-monochromatic coloring with two colors and a conflict-free coloring with three colors. We investigate generalizations of this result to colorings of objects in more complex 1-dimensional spaces, namely so-called tree spaces and planar network spaces. Keywords Conflict-free coloring • Non-monochromatic coloring • Tree • Planar networks 1 Introduction Conflict-free colorings, or CF-colorings for short, were introduced by Even et al. [8] and Smorodinsky [14] to model frequency assignment to base stations in wireless networks. In the basic setting one is given a set S of objects in the plane-often disks