Abstract
In this paper, we give an optimal χ-binding function for the class of (P7,C4,C5)-free graphs. We show that every (P7,C4,C5)-free graph G has χ(G)≤⌈119ω(G)⌉. To prove the result, we use a decomposition theorem obtained in Cameron et al. (2020) [4] combined with careful inductive arguments and a nontrivial use of the König theorem for bipartite matching.
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.
