Berge's theorem, fractional Helly, and art galleries

Abstract

Inspired by a result of Claude Berge, we prove a fractional Helly-type theorem for convex sets with starshaped unions. We also obtain a (p,3)-theorem for visibility in art galleries with a bounded number of holes, extending a result of Kalai and Matousek concerning galleries without holes.

Keywords

• Berge&apos
• s
• theorem
• fractional
• Helly
• galleries