Improved approximability and non-approximability results for graph diameter decreasing problems
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Improved approximability and non-approximability results for graph diameter decreasing problems
Theoretical Computer Science
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Alon, Gyárfás, and Ruszinkó [1] established a bound for the minimum number of edges that have to be added to a graph of n ≥ n0 vertices in order to obtain a graph of diameter 2. Alon et al. approximated n0 by a polynomial function of the maximum degree of the initial graph. They conjectured that the minimum value for n0 is 12 for the case of Cn, as opposed to n0 = 274 obtained by calculations for the general case. In this paper we prove their conjecture. For the reduction to diameter 3 of a cycle, we also improve the bounds from [1] showing that the minimum number of edges that need to be added to the cycle Cn is between n - 59 and n - 8. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 299–303, 2003