{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T08:23:39Z","timestamp":1769156619021,"version":"3.49.0"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:p> For a graph [Formula: see text] and [Formula: see text], an [Formula: see text] distance coloring is a coloring [Formula: see text] of [Formula: see text] with [Formula: see text] colors such that [Formula: see text] when [Formula: see text]. Here [Formula: see text] is the distance between [Formula: see text] and [Formula: see text] and is equal to the minimum number of edges that connect [Formula: see text] and [Formula: see text] in [Formula: see text]. The span of [Formula: see text] distance coloring of [Formula: see text], [Formula: see text], is the minimum [Formula: see text] among all [Formula: see text] distance coloring of [Formula: see text]. A class of channel assignment problem in cellular network can be formulated as a distance graph coloring problem in regular grid graphs. The cellular network is often modelled as an infinite hexagonal grid [Formula: see text], and hence determining [Formula: see text] has relevance from practical point of view. Jacko and Jendrol [Discussiones Mathematicae Graph Theory, 2005] determined the exact value of [Formula: see text] for any odd [Formula: see text] and for even [Formula: see text], it is conjectured that [Formula: see text] where [Formula: see text] is an integer, [Formula: see text] and [Formula: see text]. For [Formula: see text], the conjecture has been proved by Ghosh and Koley [[Formula: see text]nd Italian Conference on Theoretical Computer Science, 2021]. In this paper, we prove the conjecture for any even [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s012905412350020x","type":"journal-article","created":{"date-parts":[[2023,9,10]],"date-time":"2023-09-10T06:19:53Z","timestamp":1694326793000},"page":"791-813","source":"Crossref","is-referenced-by-count":1,"title":["On the Span of \u2113 Distance Coloring of Infinite Hexagonal Grid"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1778-2921","authenticated-orcid":false,"given":"Subhasis","family":"Koley","sequence":"first","affiliation":[{"name":"Techno India University, EM-4, Sector-V, Salt Lake, Kolkata 700091, WB, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3444-0333","authenticated-orcid":false,"given":"Sasthi C.","family":"Ghosh","sequence":"additional","affiliation":[{"name":"Advanced Computing and Microelectronics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India"}]}],"member":"219","published-online":{"date-parts":[[2023,9,8]]},"reference":[{"key":"S012905412350020XBIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-45208-9_13"},{"key":"S012905412350020XBIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpdc.2004.06.006"},{"key":"S012905412350020XBIB003","doi-asserted-by":"publisher","DOI":"10.26493\/1855-3974.436.178"},{"key":"S012905412350020XBIB004","first-page":"16","volume-title":"Proceedings of the 22nd Italian Conference on Theoretical Computer Science, Bologna, Italy, September 13\u201315, 2021, CEUR Workshop Proceedings","volume":"3072","author":"Ghosh S. 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