DC Field | Value | Language |
---|---|---|
dc.contributor.author | Jahanbekam, Sogol | ko |
dc.contributor.author | Kim, Jaehoon | ko |
dc.contributor.author | Suil, O. | ko |
dc.contributor.author | West, Douglas B. | ko |
dc.date.accessioned | 2019-07-18T05:34:17Z | - |
dc.date.available | 2019-07-18T05:34:17Z | - |
dc.date.created | 2019-07-17 | - |
dc.date.created | 2019-07-17 | - |
dc.date.created | 2019-07-17 | - |
dc.date.issued | 2016-06 | - |
dc.identifier.citation | DISCRETE APPLIED MATHEMATICS, v.206, pp.65 - 72 | - |
dc.identifier.issn | 0166-218X | - |
dc.identifier.uri | http://hdl.handle.net/10203/263346 | - |
dc.description.abstract | An r-dynamic proper k-coloring of a graph G is a proper k-coloring of G such that every vertex in V(G) has neighbors in at least min{d(v), r} different color classes. The r-dynamic chromatic number of a graph G, written chi(r)(G), is the least k such that G has such a coloring. By a greedy coloring algorithm, chi(r)(G) <= r Delta(G) + 1; we prove that equality holds for Delta(G) > 2 if and only if G is r-regular with diameter 2 and girth 5. We improve the bound to chi(r)(G) <= Delta(G) + 2r - 2 when delta(G) > 2r Inn and chi(r) (G) <= (G) + r when delta(G) > r(2) In n. In terms of the chromatic number, we prove X-r(G) < r chi (G) when G is k-regular with k >= (3 o(1))r In r and show that chi(r)(G) may exceed r(1.377) chi(G) when k = r. We prove chi(2) (G) <= chi (G) + 2 when G has diameter 2, with equality only for complete bipartite graphs and the 5-cycle. Also, chi(2)(G) <= 3 chi (G) when G has diameter 3, which is sharp. However, chi(2) is unbounded on bipartite graphs with diameter 4, and chi 3 is unbounded on bipartite graphs with diameter 3 or 3-colorable graphs with diameter 2. Finally, we study chi(r) on grids and toroidal grids. (C) 2016 Published by Elsevier B.V. | - |
dc.language | English | - |
dc.publisher | ELSEVIER SCIENCE BV | - |
dc.title | On r-dynamic coloring of graphs | - |
dc.type | Article | - |
dc.identifier.wosid | 000376542600007 | - |
dc.identifier.scopusid | 2-s2.0-84969361516 | - |
dc.type.rims | ART | - |
dc.citation.volume | 206 | - |
dc.citation.beginningpage | 65 | - |
dc.citation.endingpage | 72 | - |
dc.citation.publicationname | DISCRETE APPLIED MATHEMATICS | - |
dc.identifier.doi | 10.1016/j.dam.2016.01.016 | - |
dc.contributor.localauthor | Kim, Jaehoon | - |
dc.contributor.nonIdAuthor | Jahanbekam, Sogol | - |
dc.contributor.nonIdAuthor | Suil, O. | - |
dc.contributor.nonIdAuthor | West, Douglas B. | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | Dynamic coloring | - |
dc.subject.keywordAuthor | Graph coloring | - |
dc.subject.keywordPlus | CHROMATIC NUMBER | - |
dc.subject.keywordPlus | KNESER CONJECTURE | - |
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