{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T06:40:54Z","timestamp":1698043254927},"reference-count":0,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":6182,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1989,11]]},"abstract":"Abstract<\/jats:title>Let the finite, simple, undirected graph G<\/jats:italic> = (V<\/jats:italic>(G<\/jats:italic>), E<\/jats:italic>(G<\/jats:italic>)) be vertex\u2010colored. Denote the distinct colors by 1,2,\u2026,c.<\/jats:italic> Let V<\/jats:italic>i<\/jats:italic><\/jats:sub> be the set of all vertices colored j<\/jats:italic> and let <V<\/jats:italic>i<\/jats:italic><\/jats:sub> be the subgraph of G<\/jats:italic> induced by V<\/jats:italic>i<\/jats:italic><\/jats:sub>. The k<\/jats:italic>\u2010path chromatic number of G<\/jats:italic>, denoted by \u03c7(G<\/jats:italic>; P<\/jats:italic>k<\/jats:italic><\/jats:sub>), is the least number c<\/jats:italic> of distinct colors with which V<\/jats:italic>(G<\/jats:italic>) can be colored such that each connected component of V<\/jats:italic>i<\/jats:italic><\/jats:sub> is a path of order at most k<\/jats:italic>, 1 \u2a7d i \u2a7d c.<\/jats:italic> We obtain upper bounds for \u03c7(G<\/jats:italic>; P<\/jats:italic>k<\/jats:italic><\/jats:sub>) and \u03c7(G<\/jats:italic>; P<\/jats:italic>\u221e<\/jats:sub>) for regular, planar, and outerplanar graphs.<\/jats:p>","DOI":"10.1002\/jgt.3190130506","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T18:22:30Z","timestamp":1181326950000},"page":"571-573","source":"Crossref","is-referenced-by-count":11,"title":["Path chromatic numbers of graphs"],"prefix":"10.1002","volume":"13","author":[{"given":"Jin","family":"Akiyama","sequence":"first","affiliation":[]},{"given":"Hiroshi","family":"Era","sequence":"additional","affiliation":[]},{"given":"Severino V.","family":"Gervacio","sequence":"additional","affiliation":[]},{"given":"Mamoru","family":"Watanabe","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190130506","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190130506","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T02:20:57Z","timestamp":1697941257000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190130506"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,11]]},"references-count":0,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1989,11]]}},"alternative-id":["10.1002\/jgt.3190130506"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190130506","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,11]]}}}