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Partition an undirected graph of $n$ nodes into $k$ subgraphs so that total vertices inside all subgraphs is maximum.

Restriction: all subgraphs have the same number of nodes (so $k$ divides $n$); $k$ is given initially.

I'd like to receive pointers to the solution as well as papers or blogs related to or expanding on it.

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  • $\begingroup$ You might want to add the appropriate definitions to make sure we know what exact problem you are referring to. $\endgroup$ – dkaeae Feb 20 '19 at 9:28
  • $\begingroup$ Thank for pointing out. I've added the restriction. $\endgroup$ – Craneonacrane Feb 20 '19 at 9:48
  • $\begingroup$ You probably mean "total edges", not "total vertices". In any balanced partition, the total number of vertices in each part is always n/k. $\endgroup$ – Vincenzo Mar 22 '19 at 16:46
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Your problem is a special case of graph partitioning. When $k=2$, the problem is known as minimum bisection, and is NP-complete.

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