List Colorings with Distinct List Sizes, the Case of Complete Bipartite Graphs
نویسندگان
چکیده
منابع مشابه
List colorings with distinct list sizes, the case of complete bipartite graphs
Let f : V → N be a function on the vertex set of the graph G = (V,E). The graph G is f-choosable if for every collection of lists with list sizes specified by f there is a proper coloring using colors from the lists. The sum choice number, χsc(G), is the minimum of ∑ f(v), over all functions f such that G is f -choosable. It is known (Alon 1993, 2000) that if G has average degree d, then the us...
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A coloring of the vertices of a graph G is said to be distinguishing provided that no nontrivial automorphism of G preserves all of the vertex colors. The distinguishing number of G, denoted D(G), is the minimum number of colors in a distinguishing coloring of G. The distinguishing number, first introduced by Albertson and Collins in 1996, has been widely studied and a number of interesting res...
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A 2-assignment on a graph G = (V; E) is a collection of pairs L(v) of allowed colors speciied for all vertices v 2 V. The graph G (with at least one edge) is said to have oriented choice number 2 if it admits an orientation which satisses the following property : For every 2-assignment there exists a choice c(v) 2 L(v) for all v 2 V such that (i) if c(v) = c(w), then vw = 2 E, and (ii) for ever...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2015
ISSN: 0364-9024
DOI: 10.1002/jgt.21896