{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T12:59:07Z","timestamp":1772283547558,"version":"3.50.1"},"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 a graph $G$, an identifying code ${\\cal D}\\subseteq V(G)$ is a vertex set such that for any two distinct vertices $v_1,v_2\\in V(G)$, the sets $N[v_1]\\cap{\\cal D}$ and $N[v_2]\\cap{\\cal D}$ are distinct and nonempty (here $N[v]$ denotes a vertex $v$ and its neighbors).  We study the case when $G$ is the infinite hexagonal grid $H$.  Cohen et.al. constructed two identifying codes for $H$ with density $3\/7$ and proved that any identifying code for $H$ must have density at least $16\/39\\approx0.410256$. Both their upper and lower bounds were best known until now.  Here we prove a lower bound of $12\/29\\approx0.413793$.<\/jats:p>","DOI":"10.37236\/202","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:25:15Z","timestamp":1578716715000},"source":"Crossref","is-referenced-by-count":9,"title":["A New Lower Bound on the Density of Vertex Identifying Codes for the Infinite Hexagonal Grid"],"prefix":"10.37236","volume":"16","author":[{"given":"Daniel W.","family":"Cranston","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gexin","family":"Yu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2009,9,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r113\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r113\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T02:40:55Z","timestamp":1579315255000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r113"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9,18]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/202","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,9,18]]},"article-number":"R113"}}