Partitioning a graph into convex sets

@article{Artigas2011PartitioningAG,
  title={Partitioning a graph into convex sets},
  author={Danilo Artigas and Simone Dantas and Mitre Costa Dourado and Jayme Luiz Szwarcfiter},
  journal={Discrete Mathematics},
  year={2011},
  volume={311},
  pages={1968-1977}
}
Let G be a finite simple graph. Let S ⊆ V (G), its closed interval I[S] is the set of all vertices lying on a shortest path between any pair of vertices of S. The set S is convex if I[S] = S. In this work we define the concept of convex partition of graphs. If there exists a partition of V (G) into p convex sets we say that G is p-convex. We prove that is NP -complete to decide whether a graph G is p-convex for a fixed integer p ≥ 2. We show that every connected chordal graph is p-convex, for 1… CONTINUE READING

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