dc.contributor.author | Lima, Paloma T. | |
dc.contributor.author | Jaffke, Lars | |
dc.date.accessioned | 2021-06-07T10:41:33Z | |
dc.date.available | 2021-06-07T10:41:33Z | |
dc.date.created | 2020-02-19T10:12:16Z | |
dc.date.issued | 2020 | |
dc.identifier.issn | 0304-3975 | |
dc.identifier.uri | https://hdl.handle.net/11250/2758155 | |
dc.description.abstract | A b-coloring of a graph G is a proper coloring of its vertices such that each color class contains a vertex that has at least one neighbor in all the other color classes. The b-Coloring problem asks whether a graph G has a b-coloring with k colors. The b-chromatic number of a graph G, denoted by χb(G), is the maximum number k such that G admits a b-coloring with k colors. We consider the complexity of the b-Coloring problem, whenever the value of k is close to one of two upper bounds on χb(G): The maximum degree (G) plus one, and the m-degree, denoted by m(G), which is defined as the maximum number i such that G has i vertices of degree at least i −1. We obtain a dichotomy result for all fixed k ∈N when k is close to one of the two above mentioned upper bounds. Concretely, we show that if k ∈{ (G) +1 −p, m(G) −p}, the problem is polynomial-time solvable whenever p ∈{0, 1} and, even when k =3, it is NP-complete whenever p ≥2. We furthermore consider parameterizations of the b-Coloring problem that involve the maximum degree (G) of the input graph G and give two FPT-algorithms. First, we show that deciding whether a graph G has a b-coloring with m(G) colors is FPT parameterized by (G). Second, we show that b-Coloring is FPT parameterized by (G) + k(G), where k(G) denotes the number of vertices of degree at least k. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Elsevier | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | A complexity dichotomy for critical values of the b-chromatic number of graphs | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | publishedVersion | en_US |
dc.rights.holder | 2020 The Author(s). | en_US |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 2 | |
dc.identifier.doi | 10.1016/j.tcs.2020.02.007 | |
dc.identifier.cristin | 1795684 | |
dc.source.journal | Theoretical Computer Science | en_US |
dc.source.pagenumber | 182-196 | en_US |
dc.relation.project | Trond Mohn stiftelse: 810564 | en_US |
dc.relation.project | Norges forskningsråd: 249994 | en_US |
dc.identifier.citation | Theoretical Computer Science. 2020, 815, 182-196. | en_US |
dc.source.volume | 815 | en_US |