On random minimum length spanning trees

Abstract

We extend and strengthen the result that, in the complete graphK n with independent random edge-lengths uniformly distributed on [0, 1], the expected length of the minimum spanning tree tends toζ(3) asn→∞. In particular, ifK n is replaced by the complete bipartite graphK n, n then there is a corresponding limit of 2ζ (3).

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Frieze, A.M., McDiarmid, C.J.H. On random minimum length spanning trees. Combinatorica 9, 363–374 (1989). https://doi.org/10.1007/BF02125348

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AMS subject classification (1980)

  • 05C80