{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:44:08Z","timestamp":1759063448778,"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>An $r$-identifying code on a graph $G$ is a set $C\\subset V(G)$ such that for every vertex in $V(G)$, the intersection of the radius-$r$ closed neighborhood with $C$ is nonempty and unique.  On a finite graph, the density of a code is $|C|\/|V(G)|$, which naturally extends to a definition of density in certain infinite graphs which are locally finite.  We present new lower bounds for densities of codes for some small values of $r$ in both the square and hexagonal grids.<\/jats:p>","DOI":"10.37236\/394","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:10:04Z","timestamp":1578715804000},"source":"Crossref","is-referenced-by-count":6,"title":["Lower Bounds for Identifying Codes in some Infinite Grids"],"prefix":"10.37236","volume":"17","author":[{"given":"Ryan","family":"Martin","sequence":"first","affiliation":[]},{"given":"Brendon","family":"Stanton","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,9,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r122\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r122\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:27:28Z","timestamp":1579303648000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r122"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/394","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,9,13]]},"article-number":"R122"}}