{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:14:48Z","timestamp":1758824088265,"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 consider well-quasi-order for classes of permutation graphs which omit both a path and a clique. Our principle result is that the class of permutation graphs omitting $P_5$ and a clique of any size is well-quasi-ordered. This is proved by giving a structural decomposition of the corresponding permutations. We also exhibit three infinite antichains to show that the classes of permutation graphs omitting $\\{P_6,K_6\\}$, $\\{P_7,K_5\\}$, and $\\{P_8,K_4\\}$ are not well-quasi-ordered.<\/jats:p>","DOI":"10.37236\/4074","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:08:50Z","timestamp":1578701330000},"source":"Crossref","is-referenced-by-count":4,"title":["Well-Quasi-Order for Permutation Graphs Omitting a Path and a Clique"],"prefix":"10.37236","volume":"22","author":[{"given":"Aistis","family":"Atminas","sequence":"first","affiliation":[]},{"given":"Robert","family":"Brignall","sequence":"additional","affiliation":[]},{"given":"Nicholas","family":"Korpelainen","sequence":"additional","affiliation":[]},{"given":"Vadim","family":"Lozin","sequence":"additional","affiliation":[]},{"given":"Vincent","family":"Vatter","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,4,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p20\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:17:43Z","timestamp":1579256263000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i2p20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,29]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,4,14]]}},"URL":"https:\/\/doi.org\/10.37236\/4074","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,4,29]]},"article-number":"P2.20"}}