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If I have an undirected graph, G = (V, E), and I want to find the subset S of vertices in G such that all the vertices in S have at least n connections to other vertices in S. What would be the best way to do this?

Alexander
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Timothy Tran
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1 Answers1

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At first, this task sounds similar to the clique problem. Which might suggest your task will be NP-hard as well.

At second thought, it's actually much simpler and here's an algorithm:

  1. remove all v of degree less than n
  2. repeat (1) on the restricted G until it's empty or all remaining vertices have degree n or more
  3. the remaining vertices are your subset S
voidengine
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