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Combinatorica

, Volume 18, Issue 4, pp 493–501 | Cite as

How to decrease the diameter of triangle-free graphs

  • Paul Erdős
  • András Gyárfás
  • Miklós Ruszinkó
Original Paper

Assume that G is a triangle-free graph. Let \(\) be the minimum number of edges one has to add to G to get a graph of diameter at most d which is still triangle-free. It is shown that \(\) for connected graphs of order n and of fixed maximum degree. The proof is based on relations of \(\) and the clique-cover number of edges of graphs. It is also shown that the maximum value of \(\) over (triangle-free) graphs of order n is \(\). The behavior of \(\) is different, its maximum value is \(\). We could not decide whether \(\) for connected (triangle-free) graphs of order n with a positive ε.

AMS Subject Classification (1991) Classes:  05C12, 05C35 

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Copyright information

© János Bolyai Mathematical Society, 1998

Authors and Affiliations

  • Paul Erdős
  • András Gyárfás
    • 1
  • Miklós Ruszinkó
    • 2
  1. 1.Computer and Automation Research Institute of the Hungarian Academy of Sciences; Budapest, P.O.Box 63, H-1518, Hungary; E-mail: gyarfas@luna.aszi.sztaki.huHU
  2. 2.Computer and Automation Research Institute of the Hungarian Academy of Sciences; Budapest, P.O.Box 63, H-1518, Hungary; E-mail: ruszinko@lutra.sztaki.hu; recent address: Dept. of Mathematical Sciences, Carnegie Mellon University; Pittsburgh, Pennsylvania 15232, USAHU

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