Abstract
AbstractChudnovsky and Seymour proposed the Three‐in‐a‐tree algorithm which solves the following problem in polynomial time: given three fixed vertices in a simple finite graph, check whether an induced tree containing these vertices exists. In this paper, we deal with a generalization of this problem, referred to henceforth as ‐in‐a‐tree. The ‐in‐a‐tree checks whether a graph contains an induced tree spanning given vertices. When is part of the input, the problem is known to be NP‐complete. If is a fixed given number, its complexity is an open question, although there are efficient algorithms for restricted cases such as claw‐free graphs, graphs with a girth of at least and chordal graphs. We present mixed‐integer programming formulations for this problem, and we show that instances with up to 25,000 vertices can be solved in reasonable computational time.
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 callMore From: International Transactions in Operational Research
Disclaimer: 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.
