On the (n− 2)-transversals ofnconvex subsets of the plane

✍ Scribed by A. Bezdek; K. Bezdek; T. Bisztriczky

• Publisher: Springer
• Year: 1991
• Tongue: English
• Weight: 224 KB
• Volume: 40
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00189913

✦ Synopsis

In this paper we consider families of distinct ovals in the plane, with the property that certain subfamilies have stabbing lines (transversals). Our main result says that if any k member of the family can be stabbed by a line avoiding all the other ovals and k is large enough, then the family consists of at most k + 1 ovals. For any n/> 4 we show a family of n ovals, whose n-2 element subfamilies have, but the n-1 element subfamilies do not have, transversals.