On local convexity in graphs

  title={On local convexity in graphs},
  author={Martin Farber and Robert E. Jamison},
  journal={Discrete Mathematics},
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


Publications referenced by this paper.
Showing 1-10 of 16 references

Convexity in graphs and hypergraphs

  • M. Farber, R. E. Jamison
  • SIAM J. Alg. Disc. Meth. 7
  • 1986
Highly Influential
4 Excerpts

Conditions for invariance of set diameters under d-convexification in a graph

  • V. P. Soltan, V. D. Chepoi
  • Cybernetics 19
  • 1983
Highly Influential
6 Excerpts

A convexity problem in 3-polytopal graphs

  • P. Vanden Cruyce
  • Arch. Math. 43
  • 1984
1 Excerpt

d-convexity in graphs

  • V. P. Soltan
  • Soviet Math. Dold. 28
  • 1983
1 Excerpt

A perspective on abstract convexity: classifying alignments by varieties

  • R. E. Jamison
  • in: D.C. Kay and M. Breen, eds., Convexity and…
  • 1982
3 Excerpts

Similar Papers

Loading similar papers…