Introductory Combinatorics
Introductory Combinatorics
5th Edition
ISBN: 9780134689616
Author: Brualdi, Richard A.
Publisher: Pearson,
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Chapter 12, Problem 3E
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To prove: The chromatic polynomial of a disconnected graph is equal to the product of the chromatic polynomials of its connected components.

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Chapter 12 Solutions

Introductory Combinatorics

Ch. 12 - Prob. 1ECh. 12 - Prob. 2ECh. 12 - Prove that the chromatic polynomial of a...Ch. 12 - Prove that the chromatic number of a cycle graph...Ch. 12 - Prob. 5ECh. 12 - Prove that a graph with chromatic number equal to...Ch. 12 - Prove that the greedy algorithm always produces a...Ch. 12 - Let G be a graph of order n ≥ 1 with chromatic...Ch. 12 - Let G be a graph of order n whose chromatic...Ch. 12 - Prob. 10E
Ch. 12 - Prove that the chromatic polynomial of the graph...Ch. 12 - What is the chromatic number of the graph...Ch. 12 - Prob. 13ECh. 12 - Prove that the chromatic polynomial of a cycle...Ch. 12 - Prob. 15ECh. 12 - Prove that the polynomial k4 − 4k3 + 3k2 is not...Ch. 12 - Prob. 17ECh. 12 - Give an example of a planar graph with chromatic...Ch. 12 - A plane is divided into regions by a finite number...Ch. 12 - Prob. 22ECh. 12 - Prob. 23ECh. 12 - Prob. 26ECh. 12 - Let G be a planar graph of order n ≥ 2. Prove that...Ch. 12 - Find a solution to the problem of the 8 queens...Ch. 12 - Prob. 33ECh. 12 - Prob. 34ECh. 12 - Prob. 36ECh. 12 - Prob. 37ECh. 12 - Prob. 38ECh. 12 - Prob. 45ECh. 12 - Prove that the edge-connectivity of Kn equals n –...Ch. 12 - Prob. 53ECh. 12 - Prob. 54ECh. 12 - Prob. 55ECh. 12 - Determine the edge-connectivity of the complete...Ch. 12 - Prob. 63E
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