Sum-Paintability of Generalized Theta-Graphs
نویسندگان
چکیده
منابع مشابه
Sum-Paintability of Generalized Theta-Graphs
In online list coloring (introduced by Zhu and by Schauz in 2009), on each round the set of vertices having a particular color in their lists is revealed, and the coloring algorithm chooses an independent subset of this set to receive that color. For a graph G and a function f : V (G) → N, the graph is f -paintable if there is an algorithm to produce a proper coloring when each vertex v is allo...
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Harary [8] calls a finite, simple graph G a sum graph if one can assign to each vi ∈ V (G) a label xi so that {vi, vj} ∈ E(G) iff xi + xj = xk for some k. We generalize this notion by replacing “xi + xj” with an arbitrary symmetric polynomial f(xi, xj). We show that for each f , not all graphs are “f -graphs”. Furthermore, we prove that for every f and every graph G we can transform G into an f...
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Let G = (V,E) be a simple graph and for every vertex v ∈ V let L(v) be a set (list) of available colors. G is called L-colorable if there is a proper coloring φ of the vertices with φ(v) ∈ L(v) for all v ∈ V . A function f : V → N is called a choice function of G and G is said to be f -list colorable if G is L-colorable for every list assignment L with |L(v)| = f(v) for all v ∈ V . The size of ...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2014
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-014-1441-1