{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:41Z","timestamp":1753893821867,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Consider the following game between Builder and Painter. We take some families of graphs $\\mathcal{G}_{1},\\ldots,\\mathcal{G}_t$ and an integer $n$ such that $n \\geq R(\\mathcal{G}_1,\\ldots,\\mathcal{G}_t)$. In each turn, Builder picks an edge of initially uncoloured $K_n$ and Painter colours that edge with some colour $i \\in \\left\\{ 1,\\ldots,t \\right\\}$ of her choice. The game ends when a graph $G_i$ in colour $i $ for some $G_i \\in \\mathcal{G}_i$ and some $i$ is created. The restricted online Ramsey number $\\tilde{R}(\\mathcal{G}_{1},\\ldots,\\mathcal{G}_t;n)$ is the minimum number of turns that Builder needs to guarantee the game to end.\r\nIn a recent paper, Briggs and Cox studied the restricted online Ramsey numbers of matchings and determined a general upper bound for them. They proved that for $n=3r-1=R_2(r K_2)$ we have $\\tilde{R}_{2}(r K_2;n) \\leq n-1$ and asked whether this was tight. In this short note, we provide a general lower bound for these Ramsey numbers. As a corollary, we answer this question of Briggs and Cox, and confirm that for $n=3r-1$ we have $\\tilde{R}_{2}(r K_2;n) = n-1$. We also show that for $n'=4r-2=R_3(r K_2)$ we have $\\tilde{R}_{3}(r K_2;n') = 5r-4$.<\/jats:p>","DOI":"10.37236\/10025","type":"journal-article","created":{"date-parts":[[2021,7,16]],"date-time":"2021-07-16T11:17:47Z","timestamp":1626434267000},"source":"Crossref","is-referenced-by-count":0,"title":["A Note on Restricted Online Ramsey Numbers of Matchings"],"prefix":"10.37236","volume":"28","author":[{"given":"Vojt\u011bch","family":"Dvo\u0159\u00e1k","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2021,7,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i3p16\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i3p16\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,8]],"date-time":"2021-10-08T09:38:55Z","timestamp":1633685935000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i3p16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,16]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,7,1]]}},"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.37236\/10025","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,7,16]]},"article-number":"P3.16"}}