Lesson plan

Random regular graph

A random r-regular graph is a graph selected from \mathcal{G}_{n,r} , which denotes the probability space of all r-regular graphs on n vertices, where 3 \le r and nr is even. It is therefore a particular kind of random graph, but the regularity restriction significantly alters the properties that will hold, since most graphs are not regular.

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Article summary

A random r-regular graph is a graph selected from \mathcal{G}_{n,r} , which denotes the probability space of all r-regular graphs on n vertices, where 3 \le r and nr is even. It is therefore a particular kind of random graph, but the regularity restriction significantly alters the properties that will hold, since most graphs are not regular.

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Discussion questions

  1. Summarise the article in your own words. Which single claim would you verify first, and why?
  2. Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
  3. If two sources disagreed about one of these facts, what would you need in order to trust one over the other?

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