{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T08:48:03Z","timestamp":1766134083826,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We characterise the pairs of graphs $\\{ X, Y \\}$ such that all $\\{ X, Y \\}$-free graphs (distinct from $C_5$) are perfect. Similarly, we characterise pairs $\\{ X, Y \\}$ such that all $\\{ X, Y \\}$-free graphs (distinct from $C_5$) are $\\omega$-colourable (that is, their chromatic number is equal to their clique number). More generally, we show characterizations of pairs $\\{ X, Y \\}$ for perfectness and $\\omega$-colourability of all connected $\\{ X, Y \\}$-free graphs which are of independence at least~$3$, distinct from an odd cycle, and of order at least $n_0$, and similar characterisations subject to each subset of these additional constraints. (The classes are non-hereditary and the characterisations for perfectness and $\\omega$-colourability are different.) We build on recent results of Brause et al. on $\\{ K_{1,3}, Y \\}$-free graphs, and we use Ramsey's Theorem and the Strong Perfect Graph Theorem as main tools. We relate the present characterisations to known results on forbidden pairs for $\\chi$-boundedness and deciding $k$-colourability in polynomial time.<\/jats:p>","DOI":"10.37236\/10708","type":"journal-article","created":{"date-parts":[[2022,5,6]],"date-time":"2022-05-06T08:07:15Z","timestamp":1651824435000},"source":"Crossref","is-referenced-by-count":1,"title":["Forbidden Induced Pairs for Perfectness and $\\omega$-Colourability of Graphs"],"prefix":"10.37236","volume":"29","author":[{"given":"Maria","family":"Chudnovsky","sequence":"first","affiliation":[]},{"given":"Adam","family":"Kabela","sequence":"additional","affiliation":[]},{"given":"Binlong","family":"Li","sequence":"additional","affiliation":[]},{"given":"Petr","family":"Vr\u00e1na","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2022,5,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i2p21\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i2p21\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,6]],"date-time":"2022-05-06T08:07:15Z","timestamp":1651824435000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i2p21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,6]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,4,8]]}},"URL":"https:\/\/doi.org\/10.37236\/10708","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2022,5,6]]},"article-number":"P2.21"}}