Plants rooted in rocks

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.

Rooted Routing in the Plane

The problem A graph G consists of a set V G of vertices and a set E G of edges each of which is an ordered pair of vertices These objects despite their simple struc ture can be used to model important properties of a wide variety of math ematical and physical systems One of their most important applications is to the study of routing in networks Here the vertices represent sites cities computer...

Rooted k-connections in digraphs

The problem of computing a minimum cost subgraph D′ = (V,A′) of a directed graph D = (V,A) so that D′ contains k edge-disjoint paths from a specified root r ∈ V to every other node in V is known to be nicely solvable since it can be formulated as a matroid intersection problem. A corresponding problem when openly disjoint paths are requested rather than edge-disjoint was solved in [12] with the...

A characteristic polynomial for rooted graphs and rooted digraphs

We consider the one-variable characteristic polynomial p(G; ) in two settings. When G is a rooted digraph, we show that this polynomial essentially counts the number of sinks in G. When G is a rooted graph, we give combinatorial interpretations of several coe/cients and the degree of p(G; ). In particular, |p(G; 0)| is the number of acyclic orientations of G, while the degree of p(G; ) gives th...

Mulitdimensional Streams Rooted in Dataflow