A Generalization of Some Results on List Coloring and DP-Coloring
نویسندگان
چکیده
منابع مشابه
Between coloring and list-coloring: μ-coloring
A new variation of the coloring problem, μ-coloring, is defined in this paper. Given a graph G and a function μ, a μ-coloring is a coloring where each vertex v of G must receive a color at most μ(v). It is proved that μ-coloring lies between coloring and list-coloring, in the sense of generalization of problems and computational complexity. The notion of perfection is extended for μ-coloring, l...
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We study the function f G de ned for a graph G as the smallest integer k such that the join ofG with a stable set of size k is not jV G j choosable This function was introduced recently in order to describe extremal graphs for a list coloring version of a famous inequality due to Nordhaus and Gaddum Some bounds and some exact values for f G are determined
متن کاملOn a list coloring conjecture of Reed
We construct graphs with lists of available colors for each vertex, such that the size of every list exceeds the maximum vertex-color degree, but there exists no proper coloring from the lists. This disproves a conjecture of Reed. 2002 Wiley Periodicals, Inc. J Graph Theory 41: 106–109, 2002
متن کاملDynamic coloring and list dynamic coloring of planar graphs
A dynamic chromatic number χd(G) of a graph G is the least number k such that G has a proper k-coloring of the vertex set V (G) so that for each vertex of degree at least 2, its neighbors receive at least two distinct colors. We show that χd(G) ≤ 4 for every planar graph except C5, which was conjectured in [5]. The list dynamic chromatic number chd(G) of G is the least number k such that for an...
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Let G be a simple graph with n vertices and list chromatic number χl(G) = χl. Suppose that 0 ≤ t ≤ χl and each vertex of G is assigned a list of t colors. Albertson, Grossman and Haas [1] conjectured that at least tn χl vertices of G can be colored from these lists. In this paper we find some new results in partial list coloring which help us to show that the conjecture is true for at least hal...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2020
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-020-02177-6