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arXiv · 1310.7558

Coloring intersection graphs of arc-connected sets in the plane

Michał Lasoń·Piotr Micek·Arkadiusz Pawlik·Bartosz Walczak
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Abstract

A family of sets in the plane is simple if the intersection of its any subfamily is arc-connected, and it is pierced by a line $L$ if the intersection of its any member with $L$ is a nonempty segment. It is proved that the intersection graphs of simple families of compact arc-connected sets in the plane pierced by a common line have chromatic number bounded by a function of their clique number.

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Michał Lasoń, Piotr Micek, Arkadiusz Pawlik, Bartosz Walczak. 2014-08-26. Coloring intersection graphs of arc-connected sets in the plane. https://doi.org/10.1007/s00454-014-9614-5

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