Enumeration of equicolorable trees
The author defines a tree to be equicolorable if a proper bicoloring of its vertices assigns the two colors to equal numbers of vertices. It is not difficult to show that the probability that a randomly chosen (rooted or unrooted) \(n\)-vertex labelled tree is equicolorable is asymptotic to two times the probability that its vertices would be equicolored if they were assigned colors by independent coin flips. The author shows that for a randomly chosen (rooted or unrooted) \(n\)-vertex unlabelled tree the corresponding statements holds when two is replaced by \(1.40499\dots\)\ .
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