Question: This is a question about graph theory. Please use the greedy algorithm to show. Let e_{i}(G) denote the number of vertices of a graph G

This is a question about graph theory. Please use the greedy algorithm to show.

Let e_{i}(G) denote the number of vertices of a graph G whose degree is strictly greater than i. Use the greedy algorithm to show that if e_{i}(G) i + 1 for some i 1, then (G) i + 1, where (G) is the chromatic number of the graph G.

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