{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T17:22:32Z","timestamp":1771867352600,"version":"3.50.1"},"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>For ordered graphs $G$ and $H$, the ordered Ramsey number $r_&lt;(G,H)$ is the smallest $n$ such that every red\/blue edge coloring of the complete ordered graph on vertices $\\{1,\\dots,n\\}$ contains either a blue copy of $G$ or a red copy of $H$, where the embedding must preserve the relative order of vertices. One number of interest, first studied by Conlon, Fox, Lee, and Sudakov, is the off-diagonal ordered Ramsey number $r_&lt;(M, K_3)$, where $M$ is an ordered matching on $n$ vertices. In particular, Conlon et al. asked what asymptotic bounds (in $n$) can be obtained for $\\max r_&lt;(M, K_3)$, where the maximum is over all ordered matchings $M$ on $n$ vertices. The best-known upper bound is $O(n^2\/\\log n)$, whereas the best-known lower bound is $\\Omega((n\/\\log n)^{4\/3})$, and Conlon et al. hypothesize that there is some fixed $\\epsilon &gt; 0$ such that $r_&lt;(M, K_3) = O(n^{2-\\epsilon})$ for every ordered matching $M$. We resolve two special cases of this conjecture. We show that the off-diagonal ordered Ramsey numbers for ordered matchings in which edges do not cross are nearly linear. We also prove a truly sub-quadratic upper bound for random ordered matchings with interval chromatic number $2$.<\/jats:p>","DOI":"10.37236\/8085","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:14:10Z","timestamp":1578640450000},"source":"Crossref","is-referenced-by-count":6,"title":["Off-Diagonal Ordered Ramsey Numbers of Matchings"],"prefix":"10.37236","volume":"26","author":[{"given":"Dhruv","family":"Rohatgi","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,5,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p21\/7834","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p21\/7834","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:14:16Z","timestamp":1579234456000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i2p21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,17]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,4,5]]}},"URL":"https:\/\/doi.org\/10.37236\/8085","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,17]]},"article-number":"P2.21"}}