Number of maximal rooted trees in uniform attachment model via stochastic approximation

Rooted Uniform Monotone Minimum Spanning Trees

We study the construction of the minimum cost spanning geometric graph of a given rooted point set P where each point of P is connected to the root by a path that satisfies a given property. We focus on two properties, namely the monotonicity w.r.t. a single direction (y-monotonicity) and the monotonicity w.r.t. a single pair of orthogonal directions (xy-monotonicity). We propose algorithms tha...

4-PLACEMENT OF ROOTED TREES

A tree T of order n is called k-placement if there are k edge-disjoint copies of T into K_{n}. In this paper we prove some results about 4-placement of rooted trees.

Uniform Approximation and Maximal Ideal Spaces

Let X be a compact set in the z-plane. We are interested in two function spaces associated with X: C(X) — space of all continuous complex-valued functions on X. P(X) =space of all uniform limits of polynomials on X. Thus a function ƒ on X lies in P{X) if there exists a sequence {Pn} of polynomials converging to ƒ uniformly on X. Clearly P(X) is part of C(X). QUESTION I. When is P(X) = C(X)t i.e...

The Number of Rooted Trees of Given Depth

In this paper it is shown that the logarithm of the number of non-isomorphic rooted trees of depth k > 3 with n vertices is asymptotically π 2 6 · n log log... logn , where log is iterated k − 2 times in the denominator.

On the enumeration of rooted trees with fixed size of maximal decreasing trees