New results in t-tone coloring of graphs

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dc.contributor.authorCranston, Daniel W.ko
dc.contributor.authorKim, Jaehoonko
dc.contributor.authorKinnersley, William B.ko
dc.date.accessioned2019-07-18T05:34:32Z-
dc.date.available2019-07-18T05:34:32Z-
dc.date.created2019-07-17-
dc.date.created2019-07-17-
dc.date.created2019-07-17-
dc.date.issued2013-04-
dc.identifier.citationELECTRONIC JOURNAL OF COMBINATORICS, v.20, no.2-
dc.identifier.issn1077-8926-
dc.identifier.urihttp://hdl.handle.net/10203/263354-
dc.description.abstractA t-tone k-coloring of G assigns to each vertex of G a set of t colors from {1, ... , k} so that vertices at distance d share fewer than d common colors. The t-tone chromatic number of G, denoted tau(t)(G), is the minimum k such that G has a t-tone k-coloring. Bickle and Phillips showed that always tau(2)(G) <= [Delta(G)](2) + Delta(G), but conjectured that in fact tau(2)(G) <= 2 Delta(G) + 2; we confirm this conjecture when Delta(G) <= 3 and also show that always tau(2)(G) <= [(2 + root 2)Delta(G)]. For general t we prove that tau(t)(G) <= (t(2) + t)Delta(G). Finally, for each t >= 2 we show that there exist constants c(1) and c(2) such that for every tree T we have c(1)root Delta(T) <= tau(t)(T) <= c(2)root Delta(T).-
dc.languageEnglish-
dc.publisherELECTRONIC JOURNAL OF COMBINATORICS-
dc.titleNew results in t-tone coloring of graphs-
dc.typeArticle-
dc.identifier.wosid000318227600005-
dc.type.rimsART-
dc.citation.volume20-
dc.citation.issue2-
dc.citation.publicationnameELECTRONIC JOURNAL OF COMBINATORICS-
dc.contributor.localauthorKim, Jaehoon-
dc.contributor.nonIdAuthorCranston, Daniel W.-
dc.contributor.nonIdAuthorKinnersley, William B.-
dc.description.isOpenAccessN-
dc.type.journalArticleArticle-
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