Random Minimum Length Spanning Trees in Regular Graphs

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 that mst(G) can be estimated quite accurately under two distinct circumstances. Firstly, if r is large and G has a modest edge expansion property then , where . Secondly, if G has large girth then there exists an explicitly defined constant such that . We find in particular that .

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Received: Februray 9, 1998

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Beveridge, A., Frieze, A. & McDiarmid, C. Random Minimum Length Spanning Trees in Regular Graphs. Combinatorica 18, 311–333 (1998). https://doi.org/10.1007/PL00009825

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  • AMS Subject Classification (1991) Classes:  05C80, 60C05