How Do You Solve Calculus Homework Problem Six Using LaTeX?

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Homework Statement
Use to start learning calculus
Relevant Equations
In short, the knowledge of calculus is fine, but it is as simple as possible, not a mathematics major, before starting to learn calculus
How to solve the sixth problem?
 

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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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