On local convexity in graphs

@article{Farber1987OnLC,
  title={On local convexity in graphs},
  author={Martin Farber and Robert E. Jamison},
  journal={Discrete Mathematics},
  year={1987},
  volume={66},
  pages={231-247}
}
A set K of nodes of a graph G is geodesically convex (respectively, monophonically convex) if K contains every node on every shortest (respectively, chordless) path joining nodes in K. We investigate the classes of graphs which are characterized by certain local convexity conditions with respect to geodesic convexity, in particular, those graphs in which balls around nodes are convex, and those graphs in which neighborhoods of convex sets are convex. For monophonic convexity, these conditions… CONTINUE READING

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