{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:12Z","timestamp":1753893792182,"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 introduce the random graph $\\mathcal{P}(n,q)$ which results from taking the union of two paths of length $n\\geq 1$, where the vertices of one of the paths have been relabelled according to a Mallows permutation with real parameter $0&lt;q(n)\\leq 1$. This random graph model, the tangled path, goes through an evolution: if $q$ is close to $0$ the graph bears resemblance to a path and as $q$ tends to $1$ it becomes an expander. In an effort to understand the evolution of $\\mathcal{P}(n,q)$ we determine the treewidth and cutwidth of $\\mathcal{P}(n,q)$ up to log factors for all $q$. We also show that the property of having a separator of size one has a sharp threshold. In addition, we prove bounds on the diameter, and vertex isoperimetric number for specific values of $q$.<\/jats:p>","DOI":"10.37236\/11602","type":"journal-article","created":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T14:33:13Z","timestamp":1747924393000},"source":"Crossref","is-referenced-by-count":0,"title":["Tangled Paths: A Random Graph Model from Mallows Permutations"],"prefix":"10.37236","volume":"32","author":[{"given":"Jessica","family":"Enright","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kitty","family":"Meeks","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"William","family":"Pettersson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John","family":"Sylvester","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2025,5,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i2p35\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i2p35\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T14:33:14Z","timestamp":1747924394000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i2p35"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,23]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,4,11]]}},"URL":"https:\/\/doi.org\/10.37236\/11602","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2025,5,23]]},"article-number":"P2.35"}}