{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:39:14Z","timestamp":1740155954552,"version":"3.37.3"},"reference-count":6,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2018,4]]},"abstract":"<jats:p> Let [Formula: see text] be a graph and [Formula: see text] a non-negative integer. Suppose [Formula: see text] is a mapping from the vertex set of [Formula: see text] to [Formula: see text]. If, for any vertex [Formula: see text] of [Formula: see text], the number of neighbors [Formula: see text] of [Formula: see text] with [Formula: see text] is less than or equal to [Formula: see text], then [Formula: see text] is called a [Formula: see text]-relaxed [Formula: see text]-coloring of [Formula: see text]. And [Formula: see text] is said to be [Formula: see text]-colorable. The [Formula: see text]-relaxed chromatic number of [Formula: see text], denote by [Formula: see text], is defined as the minimum integer [Formula: see text] such that [Formula: see text] is [Formula: see text]-colorable. Let [Formula: see text] and [Formula: see text] be two positive integers with [Formula: see text]. Denote by [Formula: see text] the path on [Formula: see text] vertices and by [Formula: see text] the [Formula: see text]th power of [Formula: see text]. This paper determines the [Formula: see text]-relaxed chromatic number of [Formula: see text] the [Formula: see text]th power of [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830918500179","type":"journal-article","created":{"date-parts":[[2018,1,15]],"date-time":"2018-01-15T04:38:24Z","timestamp":1515991104000},"page":"1850017","source":"Crossref","is-referenced-by-count":0,"title":["On t-relaxed chromatic number of r-power paths"],"prefix":"10.1142","volume":"10","author":[{"given":"Jun","family":"Lan","sequence":"first","affiliation":[{"name":"Institute of Desert Meteorology, China Meteorological Administration, Urumqi 830002, P. R. China"},{"name":"School of Mathematics, Southeast University, Nanjing 210096, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4112-0469","authenticated-orcid":false,"given":"Wensong","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Mathematics, Southeast University, Nanjing 210096, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,4,2]]},"reference":[{"key":"S1793830918500179BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.jda.2012.07.001"},{"key":"S1793830918500179BIB002","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190100207"},{"key":"S1793830918500179BIB003","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0118(199703)24:3<205::AID-JGT2>3.0.CO;2-T"},{"key":"S1793830918500179BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(94)90260-7"},{"key":"S1793830918500179BIB005","doi-asserted-by":"publisher","DOI":"10.1002\/net.20318"},{"key":"S1793830918500179BIB006","first-page":"237","volume":"1","author":"Lov\u00e1sz L.","year":"1966","journal-title":"Studia Sci. Math. Hungar."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830918500179","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T11:05:26Z","timestamp":1565175926000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830918500179"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4]]},"references-count":6,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2018,4,2]]},"published-print":{"date-parts":[[2018,4]]}},"alternative-id":["10.1142\/S1793830918500179"],"URL":"https:\/\/doi.org\/10.1142\/s1793830918500179","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2018,4]]}}}