Abstract
In a graph G = ( V, E) provided with a linear order ‘ < ’ on V, a chordless path with vertices a, b, c, d and edges ab, bc, cd is called an obstruction if both a < b and d < c hold. Chvátal (1984) defined the class of perfectly orderable graphs (i.e., graphs possessing an acyclic orientation of the edges such that no obstruction is induced) and proved that they are perfect. We introduce here the class of properly orderable graphs which is a generalization of Chvátal's class of perfectly orderable graphs: obstructions are forbidden only in the subgraphs induced by the vertices of an odd cycle. We prove the perfection of these graphs and give an O( m 2 + mn + n) colouring algorithm.
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.
