A helly number for unions of two boxes in R 2

Marilyn Breen

International Journal of Mathematics and Mathematical Sciences, 1985, vol. 8, 1-7

Abstract:

Let S be a polygonal region in the plane with edges parallel to the coordinate axes. If every 5 or fewer boundary points of S can be partitioned into sets A and B so that conv A ⋃ conv B ⫅ S , then S is a union of two convex sets, each a rectangle. The number 5 is best possible.

Without suitable hypothesis on edges of S , the theorem fails. Moreover, an example reveals that there is no finite Helly number which characterizes arbitrary unions of two convex sets, even for polygonal regions in the plane.

Date: 1985
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/8/212093.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/8/212093.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:212093

DOI: 10.1155/S0161171285000291

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().