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Weak Coloring: Graph Theory, Graph Labeling -

English
2026-03-20
€156.58 €195.73

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High Quality Content by WIKIPEDIA articles! A graph vertex coloring is a weak coloring, but not necessarily vice versa. Every graph has a weak 2-coloring. The figure on the right illustrates a simple algorithm for constructing a weak 2-coloring in an arbitrary graph. Part (a) shows the original graph. Part (b) shows a breadth-first search tree of the same graph. Part (c) shows how to color the tree: startin ... Full description

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High Quality Content by WIKIPEDIA articles! A graph vertex coloring is a weak coloring, but not necessarily vice versa. Every graph has a weak 2-coloring. The figure on the right illustrates a simple algorithm for constructing a weak 2-coloring in an arbitrary graph. Part (a) shows the original graph. Part (b) shows a breadth-first search tree of the same graph. Part (c) shows how to color the tree: starting from the root, the layers of the tree are colored alternatingly with colors 1 (dark) and 2 (light). If there is no isolated vertex in the graph G, then a weak 2-coloring determines a domatic partition: the set of the nodes with c(v) = 1 is a dominating set, and the set of the nodes with c(v) = 2 is another dominating set.

More Information

Publisher OmniScriptum
Release year 2026
Cover type Softcover
EAN 9786131190704
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€156.58 €195.73