Shelah’s Revised Gch and a Question by Alon
نویسنده
چکیده
The list-chromatic number χ`(G) of a graph G = (V,E) is the least cardinal κ such that for every assignment of a list L(V ) of at least κ colors to each vertex v ∈ V there is a proper vertex coloring c of G assigning to each vertex v a color from its list L(V ). The coloring number of G is the least cardinal κ such that there exists a well-ordering ≺ of V with the property that |{u : {u, v} ∈ E and u ≺ v}| < κ for every vertex v ∈ V . N. Alon proved in [2] that the coloring number of a finite graph satisfies
منابع مشابه
Shelah’s Revised Gch Theorem and a Question by Alon on Infinite Graphs Colorings
For every graph G, the coloring number of G does not exceed the least strong limit cardinal above the graph’s list-chromatic number.
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