About: Equitable d-degenerate Choosability of Graphs

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An Entity of Type : schema:ScholarlyArticle, within Data Space : covidontheweb.inria.fr associated with source document(s)

Attributes	Values
type	Academic Article research paper schema:ScholarlyArticle
isDefinedBy	Covid-on-the-Web dataset
has title	Equitable d-degenerate Choosability of Graphs
Creator	Drgas-Burchardt, Ewa Furmańczyk, Hanna Sidorowicz, Elżbieta
Source	PMC
abstract	Let [Formula: see text] be the class of d-degenerate graphs and let L be a list assignment for a graph G. A colouring of G such that every vertex receives a colour from its list and the subgraph induced by vertices coloured with one color is a d-degenerate graph is called the [Formula: see text]-colouring of G. For a k-uniform list assignment L and [Formula: see text], a graph G is equitably [Formula: see text]-colorable if there is an [Formula: see text]-colouring of G such that the size of any colour class does not exceed [Formula: see text]. An equitable [Formula: see text]-colouring is a generalization of an equitable list coloring, introduced by Kostochka et al., and an equitable list arboricity presented by Zhang. Such a model can be useful in the network decomposition where some structural properties on subnets are imposed. In this paper we give a polynomial-time algorithm that for a given (k, d)-partition of G with a t-uniform list assignment L and [Formula: see text], returns its equitable [Formula: see text]-colouring. In addition, we show that 3-dimensional grids are equitably [Formula: see text]-colorable for any t-uniform list assignment L where [Formula: see text].
has issue date	2020-04-30(xsd:dateTime)
bibo:doi	10.1007/978-3-030-48966-3_19
has license	no-cc
sha1sum (hex)	dddccf91be0bed6a4aa950d2cb6484cd8c2d30e0
schema:url	https://doi.org/10.1007/978-3-030-48966-3_19
resource representing a document's title	Equitable d-degenerate Choosability of Graphs
has PubMed Central identifier	PMC7254909
schema:publication	Combinatorial Algorithms
resource representing a document's body	covid:dddccf91be0bed6a4aa950d2cb6484cd8c2d30e0#body_text
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