Abstract
The art gallery theorem asserts that any polygon with n vertices can be protected by at most ⌊n/3⌋ stationary guards. The original proof by Chvátal uses a nonroutine and nonintuitive induction. We give a simple inductive proof of a new, more general result, the constrained art gallery theorem: If V* and E* are specified sets of vertices and edges that must contain guards, then the polygon can be protected by at most ⌊(n + 2|V*| + |E*|)/3⌋ guards. Our result reduces to Chvátal's art gallery theorem when V* and E* are empty. We give a second short proof of this generalization in the spirit of Fisk's proof of the art gallery theorem using graph colorings.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
