Abstract
In this paper we show that for n-vertex graphs with maximum degree 3, and for any fixed ε> 0, it is NP-hard to find α-edge separators and α-vertex separators of size no more than OPT+ n 1 2 − ε , where OPT is the size of the optimal solutio n. For general graphs we show that it is NP-hard to find an α-edge separator of size no more than OPT+ n 2 - ε. We also show that an O(ƒ( n))-approximation algorithm for finding α-vertex separators of maximum degree 3 graphs can be used to find an O(ƒ( n 5))-approximation algorithm for finding α-edge separators of general graphs. Since it is NP-hard to find optimal α-edge separators for general graphs this means that it is NP-hard to find optimal vertex separators even when restricted to maximum degree 3 graphs.
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.
