How Do Exponential and Radical Properties Solve Textbook Problems?

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So this is what I have tried so far playing around with exponent and radical properties to try and solve this textbook problem
 

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Homework and problems from textbooks must be posted in the Homework & Coursework section. I have moved this thread.
 
Thanks. Sorry the picture is not orientated properly the PF app isn't playing nice...
 
Try doing a substitution.
 
Figured it out actually. Turns out I read the problem wrong. Thanks tho.
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...
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