3 research outputs found
Random subtrees of complete graphs
We study the asymptotic behavior of four statistics associated with subtrees
of complete graphs: the uniform probability that a random subtree is a
spanning tree of , the weighted probability (where the probability a
subtree is chosen is proportional to the number of edges in the subtree) that a
random subtree spans and the two expectations associated with these two
probabilities. We find and both approach ,
while both expectations approach the size of a spanning tree, i.e., a random
subtree of has approximately edges