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

It is well known that any set of n intervals in \(\mathbb {R} ^1\) 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.

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