Abstract
Abstract
We prove that the intersection hypergraph of a family of n pseudo-disks with respect to another family of pseudo-disks admits a proper coloring with four colors and a conflict-free coloring with $$O(\log n)$$
O
(
log
n
)
colors. Along the way we prove that the respective Delaunay-graph is planar. We also prove that the intersection hypergraph of a family of n regions with linear union complexity with respect to a family of pseudo-disks admits a proper coloring with constantly many colors and a conflict-free coloring with $$O(\log n)$$
O
(
log
n
)
colors. Our results serve as a common generalization and strengthening of many earlier results, including ones about proper and conflict-free coloring points with respect to pseudo-disks, coloring regions of linear union complexity with respect to points and coloring disks with respect to disks.
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Theoretical Computer Science
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