{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:45:08Z","timestamp":1759063508814,"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>An $r$-identifying code in a graph $G = (V,E)$ is a subset $C \\subseteq V$ such that for each $u \\in V$ the intersection of $C$ and the ball of radius $r$ centered at $u$ is non-empty and unique. Previously, $r$-identifying codes have been studied in various grids. In particular, it has been shown that there exists a $2$-identifying code in the hexagonal grid with density $4\/19$ and that there are no $2$-identifying codes with density smaller than $2\/11$. Recently, the lower bound has been improved to $1\/5$ by Martin and Stanton (2010). In this paper, we prove that the $2$-identifying code with density $4\/19$ is optimal, i.e. that there does not exist a $2$-identifying code in the hexagonal grid with smaller density.<\/jats:p>","DOI":"10.37236\/2414","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:27:20Z","timestamp":1578713240000},"source":"Crossref","is-referenced-by-count":4,"title":["Optimal Lower Bound for 2-Identifying Codes in the Hexagonal Grid"],"prefix":"10.37236","volume":"19","author":[{"given":"Ville","family":"Junnila","sequence":"first","affiliation":[]},{"given":"Tero","family":"Laihonen","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2012,6,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i2p38\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i2p38\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:33:33Z","timestamp":1579300413000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i2p38"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,13]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2012,4,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2414","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,6,13]]},"article-number":"P38"}}