An internal partition of a graph G= (V, E) is a partitioning of V into two parts such that every vertex has at least a half of its neighbors on its own side. We prove that for every positive integer r, asymptotically almost every 2r-regular graph has an internal partition. Whereas previous results in this area apply only to a small fraction of all 2r-regular graphs, ours applies to almost all of them.
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- Graph partitions
- Internal partition
- Satisfactory partition
- Vertex degree