Adaptable chromatic number of graph products
نویسندگان
چکیده
منابع مشابه
The Adaptable Chromatic Number and the Chromatic Number
We prove that the adaptable chromatic number of a graph is at least asymptotic to the square root of the chromatic number. This is best possible. Consider a graph G where each edge of G is assigned a colour from {1, ..., k} (this is not necessarily a proper edge colouring). A k-adapted colouring is an assignment of colours from {1, ..., k} to the vertices of G such that there is no edge with th...
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A b-coloring is a proper vertex coloring of a graph such that each color class contains a vertex that has a neighbor in all other color classes and the b-chromatic number is the largest integer φ(G) for which a graph has a bcoloring with φ(G) colors. We determine some upper and lower bounds for the b-chromatic number of the strong product G H, the lexicographic product G[H] and the direct produ...
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It is shown that the difference between the chromatic number χ and the fractional chromatic number χf can be arbitrarily large in the class of uniquely colorable, vertex transitive graphs. For the lexicographic product G ◦ H it is shown that χ(G ◦ H) ≥ χf (G)χ(H). This bound has several consequences, in particular it unifies and extends several known lower bounds. Lower bounds of Stahl (for gen...
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The adaptable chromatic number of a graph G is the smallest integer k such that for any edge k-colouring of G there exists a vertex kcolouring of G in which the same colour never appears on an edge and both its endpoints. (Neither the edge nor the vertex colourings are necessarily proper in the usual sense.) We give an efficient characterization of graphs with adaptable chromatic number at most...
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given a graph $g$, the total dominator coloring problem seeks aproper coloring of $g$ with the additional property that everyvertex in the graph is adjacent to all vertices of a color class. weseek to minimize the number of color classes. we initiate to studythis problem on several classes of graphs, as well as findinggeneral bounds and characterizations. we also compare the totaldominator chro...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.05.029