On staircase starshapedness in rectilinear spaces

✍ Scribed by Victor Chepoi

• Publisher: Springer
• Year: 1996
• Tongue: English
• Weight: 508 KB
• Volume: 63
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00181420

✦ Synopsis

Let P C ~'~ be a union of a finite number of boxes whose intersection graph is a tree. If every two boundary points of P are visible via staircase paths from a common point of P, then P is starshaped via staircase paths. The same result holds true when P is a cubical polyhedron of ~'~, which is the geometric realization of some median graph.

This generalizes the recent result of M. Breen, J. Geometry, 51 (1994), established for simple rectilinear polygons.