{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:57Z","timestamp":1753893837018,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The bipartite Ramsey number $b(s,t)$ is the smallest integer $n$ such that every blue-red edge coloring of $K_{n,n}$ contains either a blue $K_{s,s}$ or a red $K_{t,t}$. In the bipartite $K_{2,2}$-free process, we begin with an empty graph on vertex set $X\\cup Y$, $|X|=|Y|=n$. At each step, a random edge from $X\\times Y$ is added under the restriction that no $K_{2,2}$ is formed. This step is repeated until no more edges can be added. In this note, we analyze this process and prove that the resulting graph shows that $b(2,t) =\\Omega(t^{3\/2}\/\\log t)$, thereby improving the best known lower bound.<\/jats:p>","DOI":"10.37236\/9101","type":"journal-article","created":{"date-parts":[[2020,10,30]],"date-time":"2020-10-30T08:55:37Z","timestamp":1604048137000},"source":"Crossref","is-referenced-by-count":0,"title":["The Bipartite $K_{2,2}$-Free Process and Bipartite Ramsey Number $b(2, t)$"],"prefix":"10.37236","volume":"27","author":[{"given":"Deepak","family":"Bal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Patrick","family":"Bennett","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,10,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p23\/8204","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p23\/8204","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,30]],"date-time":"2020-10-30T08:55:37Z","timestamp":1604048137000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i4p23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,30]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/9101","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,10,30]]},"article-number":"P4.23"}}