{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:47Z","timestamp":1753893827449,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Given $n$ sets $X_1,\\ldots, X_n$, we call the elements of $S=X_1\\times\\cdots\\times X_n$ strings. A nonempty set of strings $W\\subseteq S$ is said to be well-connected\u00a0if for every $v\\in W$ and for every $i\\, (1\\le i\\le n)$, there is another element $v'\\in W$ which differs from $v$ only in its $i$th coordinate. We prove a conjecture of Yaokun Wu and Yanzhen Xiong by showing that every set of more than $\\prod_{i=1}^n|X_i|-\\prod_{i=1}^n(|X_i|-1)$ strings has a well-connected subset. This bound is tight.<\/jats:p>","DOI":"10.37236\/10291","type":"journal-article","created":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T00:51:13Z","timestamp":1649033473000},"source":"Crossref","is-referenced-by-count":2,"title":["On Well-Connected Sets of Strings"],"prefix":"10.37236","volume":"29","author":[{"given":"Peter","family":"Frankl","sequence":"first","affiliation":[]},{"given":"J\u00e1nos","family":"Pach","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2022,3,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i1p56\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i1p56\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T00:51:13Z","timestamp":1649033473000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i1p56"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1,27]]}},"URL":"https:\/\/doi.org\/10.37236\/10291","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2022,3,25]]},"article-number":"P1.56"}}