Yevgeniy Kovchegov, Peter T. Otto, Anatoly Yambartsev
Published 2017-02-24Version 1
In this paper we devise a method of finding the limiting mean length of a minimal spanning tree for a random graph via the Smoluchowski coagulation equations for the corresponding coalescent process. In particular, we use this approach for finding the limiting mean length of a minimal spanning tree for the Erdos-Renyi random graph on an asymmetric bipartite graph, producing a completely new formula yet consistent with the previously known formula for the symmetric bipartite graph $K_{n,n}$.
Geometry of the minimal spanning tree of a random $3$-regular graph
Polynomial representation for the expected length of minimal spanning trees
Geometry of the minimal spanning tree in the heavy-tailed regime: new universality classes
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