Question
Prove that the chromatic number of a disconnected graph is the largest of the chromatic numbers of its connected components.
Step 1
First, let's recall the definition of the chromatic number of a graph. The chromatic number of a graph G, denoted by χ(G), is the smallest number of colors needed to color the vertices of G in such a way that no two adjacent vertices share the same color. Show more…
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Show that the edge chromatic number of a graph must be at least as large as the maximum degree of a vertex of the graph.
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