Answers are grounded in this paper and cite their sources.
How small can the diameter be made by adding a matching to an n-cycle? In this paper this question is answered by showing that the graph consisting ofan n-cycle and a random matching has diameter about log2n, which is very close to the best possible value. It is also shown that by adding a random matching to graphs with certain expanding properties such as expanders or Ramanujan graphs, the resulting graphs have near optimum diameters.
No takes yet. Share an insight, caveat, or question.
Bollobás et al. (1988) studied this question.
Synapse has enriched 10 related papers. Consider them for comparative context: