On the Length of a Random Minimum Spanning Tree

We study the expected value of the length Ln of the minimum spanning tree of the complete graph Kn when each edge e is given an independent uniform [0, 1] edge weight. We sharpen the result of Frieze [6] that limn→∞ E(Ln) = ζ(3) and show that E(Ln) = ζ(3) + c1 n + c2+o(1) n4/3 where c1, c2 are explicitly defined constants. AMS Classification: 05C80, 05C85.

• Type: Journal
• Year: 2016
• Where: CPC
• Authors: Colin Cooper, Alan M. Frieze, Nate Ince, Svante Janson, Joel Spencer
• Keywords: Artificial Intelligence, CPC 2016