Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Faculty Publications Article Faculty Publications -Articles Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Creator An entity primarily responsible for making the resource Angeliya, C.U.; Choudum, Sheshayya; Joseph, Mayamma Title A name given to the resource Chromatic bounds of some (P5, banner)-free graphs Date A point or period of time associated with an event in the lifecycle of the resource 01-01-2026 Source A related resource from which the described resource is derived Asian-European Journal of Mathematics;Issue;;Article No.;2650025; Identifier An unambiguous reference to the resource within a given context <a href="https://doi.org/10.1142/S1793557126500257" target="_blank" rel="noreferrer noopener">https://doi.org/10.1142/S1793557126500257</a> <br /><br /><a href="https://www.scopus.com/pages/publications/105032237008?origin=resultslist" target="_blank" rel="noreferrer noopener">https://www.scopus.com/pages/publications/105032237008?origin=resultslist</a> Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Angeliya C.U., Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bangalore, 560029, India; Choudum S., Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bangalore, 560029, India; Joseph M., Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bangalore, 560029, India Description An account of the resource Let ?(G) and ?(G), respectively, denote the chromatic number and clique number of a graph G. A P5 is a path on five vertices, a banner (paw) is the graph obtained by joining a new vertex to a single vertex of C4 (C3) and a hammer is obtained by subdividing the pendant edge of a paw exactly once. Recently, (P5,banner)-free graphs have received wide attention. In 2019, Karthick, Maffray and Pastor, gave a structural characterisation of (P5,banner)-free graphs, which when combined with a result by Bourneuf and Thomass[Bounded twin-width graphs are polynomially ?-bounded, Adv. Comb. (2025)] implies that for a (P5,banner)-free graph G, ?(G) ? ?(G)5. Geir [Colourings of P5-Free Graphs, PhD Thesis, Technische Universit at Bergakademie Freiberg (2022)] showed that the ?-binding function of the class of (P5,banner)-free graphs is bounded by the ?-binding function of 3K1-free graphs. By a result of Kim [The Ramsey number R(3,t) has order of magnitude t2/log t, Random Structures and Algorithms 7(3) (1995) 173207], the chromatic number ?(G) of a 3K1-free graph G has order of magnitude ?(?(G)2/log ?(G)). Recently, Song and Xu [Divisibility and coloring of some P5-free graphs, Discrete Appl. Math. 348 (2024) 144151] proved that every (P5, C5, banner, hammer)-free graph G is ?(G)3/2-colorable. This motivates us to study the subclasses of (P5, banner)-free graphs. We prove that for any (P5, banner, F ? K1)-free graph G where F ?{C4,K4 ? e,K3 ? K1,paw}, ?(G) ? ?(G)2/2 for ?(G) ? 3. Moreover, the bound is tight for ?(G) = 3. 2026 World Scientific Publishing Company. Subject The topic of the resource (P₅, banner)-free graphs; chromatic number; clique number; Graph classes Publisher An entity responsible for making the resource available World Scientific Relation A related resource ISSN: 17935571; Language A language of the resource English Type The nature or genre of the resource Article Rights Information about rights held in and over the resource Restricted Access; Hardcopy may be available in the library Format The file format, physical medium, or dimensions of the resource online