A Note on Random Minimum Length Spanning Trees

Consider a connected r-regular n-vertex graph G with random independent edge lengths, each uniformly distributed on [0, 1]. Let mst(G) be the expected length of a minimum spanning tree. We show in this paper that if G is sufficiently highly edge connected then the expected length of a minimum spanning tree is n r (3). If we omit the edge connectivity condition, then it is at most n r ((3) + 1).

• Type: Journal
• Year: 2000
• Where: COMBINATORICS
• Authors: Alan M. Frieze, Miklós Ruszinkó, Lubos Thoma
• Keywords: COMBINATORICS 2000, Edge, Independent Edge Lengths, R-regular N-vertex Graph