A note on weighted rooted trees

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.

A NOTE ON THE EQUISEPARABLE TREES

Let T be a tree and n_{l}(eIT) and n_{2}(eIT) denote the number of vertices of T, lying on the two sides of the edge e. Suppose T_{l} and T_{2} are two trees with equal number of vertices, e in T_{1} and f in T_{2}. The edges e and f are said to be equiseparable if either n_{l}(eIT_{I}) = n_{l}(fIT_{2}) or n_{l}(eIT_{I}) = n_{2}(fIT_{2}). If there is an one-to-one correspondence between the ver...

A note on Rooted Survivable Networks

The (undirected) Rooted Survivable Network Design (Rooted SND) problem is: given a complete graph on node set V with edge-costs, a root s ∈ V , and (node-)connectivity requirements {r(t) : t ∈ T ⊆ V }, find a minimum cost subgraph G that contains r(t) internally-disjoint st-paths for all t ∈ T . For large values of k = maxt∈T r(t) Rooted SND is at least as hard to approximate as Directed Steine...

A Note on Weighted Composition Operators on L^p-Spaces

Random Walks on Rooted Trees

For arbitrary positive integers h and m, we consider the family of all rooted trees of height h having exactly m vertices at distance h from the root. We refer to such trees as (h,m)-trees. For a tree T from this family, we consider a simple random walk on T which starts at the root and terminates when it visits one of the m vertices at distance h from the root. Consider the problem of finding ...