Week 9 practice problems

Chromatic number and index

Find the chromatic number $\chi(G)$ and the chromatic index $\chi^\prime(G)$ for the following graphs:

A word problem

Eleven football games are to be arranged among eight temas A to H as follows:

• A plays F, G, H
• B plays E, F, H
• D plays C, E, G
• E plays G
• F plays H

If no team can play more than onces a week, what is the minimum number of weeks needed to schedule all the games? Justify your answer.