English

Coloring intersection graphs of arc-connected sets in the plane

Combinatorics 2014-08-27 v3 Computational Geometry Discrete Mathematics

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 LL if the intersection of its any member with LL 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.

Keywords

Cite

@article{arxiv.1310.7558,
  title  = {Coloring intersection graphs of arc-connected sets in the plane},
  author = {Michał Lasoń and Piotr Micek and Arkadiusz Pawlik and Bartosz Walczak},
  journal= {arXiv preprint arXiv:1310.7558},
  year   = {2014}
}

Comments

Minor changes + some additional references not included in the journal version

R2 v1 2026-06-22T01:55:50.303Z