Abstract
A graph is a P4-indifference graph if it admits an ordering < on its vertices such that every chordless path with vertices a, b, c, d and edges ab, bc, cd has a
Highlights
A P4 is a chordless path of four vertices
This paper shows how a linear time algorithm for the P4-indifference graphs recognition can be designed
This algorithm strongly relies on modular decomposition as a preprocessing
Summary
A graph is P4-indifference if it admits an ordering on its vertex set such that every P4 abcd has a b c d or d c b a. The first recognition algorithm for P4-indifference graphs is due to Hoang and Reed and has the complexity of On6μ [HR89] They compute the equivalence classes of some relation on the P4’s of the graph. Hoang, Maffray and Noy gave a characterization by forbidden induced subgraphs [HMN99] and raised the question of the existence of a linear time recognition algorithm. We answer their question in the affirmative way using some of their theorems. 1365–8050 c 2001 Maison de l’Informatique et des Mathematiques Discretes (MIMD), Paris, France
Sign-in/Register to view highlights & summary 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: Discrete Mathematics & Theoretical Computer Science
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.
