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Sep 19, 2018 at 14:39 comment added Gerhard Paseman I am not a graph theorist and do not know the literature, so I have no references for you right now. Except for the case of n-1 edges, there is no guarantee on the minimum number of edges. However, this shows that d has to be greater than 2 and less than log n in order for finding the minimum number of edges to be a challenge, when given k as a restriction. For searching, the only non-obvious suggestion I have is to try literature on computer networking. Gerhard "Surely Someone Did This Already" Paseman, 2018.09.19.
Sep 19, 2018 at 12:16 comment added TheRacoonOfDeath Thank you for your answer. Is this construction guaranteed to lead to the graph with the minimum number of edges? Are there references you can recommend?
Sep 14, 2018 at 17:12 history edited Gerhard Paseman CC BY-SA 4.0
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Sep 14, 2018 at 17:07 history answered Gerhard Paseman CC BY-SA 4.0