Coloring intersection graphs of arc-connected sets in the plane

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.

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

References in corpus (2)

• Triangle-free intersection graphs of line segments with large chromatic number
• Triangle-free geometric intersection graphs with large chromatic number

Cited by in corpus (2)

• New bounds on the maximum number of edges in $k$-quasi-planar graphs
• Coloring triangle-free rectangle overlap graphs with $O(\log \log n)$ colors