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16. Give an example of a graph that requires five colors to make a valid coloring. (Note that, by the Four Color Theorem, your example cannot be planar.)

16. Give an example of a graph that requires five colors to make a valid coloring. (Note that, by the Four Color Theorem, your example cannot be planar.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 16

15. Using as few groups as possible, put the words fish, sit, stay, play, diet, tree, duck, dog, and hen into groups such that none of the words in a group have any letters in common. Use a graph model and graph coloring. Justify your answer: explain why your grouping uses the fewest groups possible. 16. Give an example of a graph that requires five colors to make a valid coloring. (Note that, by the Four Color Theorem, your example cannot be planar.) 17. Compute the minimal number of colors needed to color the following graph. Show that your answer is big enough (by describing a coloring), and explain why the graph cannot be colored in fewer colors.
Transcribed Image Text:15. Using as few groups as possible, put the words fish, sit, stay, play, diet, tree, duck, dog, and hen into groups such that none of the words in a group have any letters in common. Use a graph model and graph coloring. Justify your answer: explain why your grouping uses the fewest groups possible. 16. Give an example of a graph that requires five colors to make a valid coloring. (Note that, by the Four Color Theorem, your example cannot be planar.) 17. Compute the minimal number of colors needed to color the following graph. Show that your answer is big enough (by describing a coloring), and explain why the graph cannot be colored in fewer colors.
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