
The edge-integrity of a graph
where
Let
The numbers of sets of independent edge sets in
It is well-known that if
If
This paper looks at the problem of determining when
A complete answer is given for
A partial answer is given for
Given a set of
This intriguing optimization problem is known as the Steiner Minimal Tree Problem (SMT), where the junctions that are added to the network are called Steiner Points.
The focus of this paper is twofold.
First We look at the computational history of the problem, up through and including a new method to compute SMT’s in parallel.
Secondly We look at future work in the computation of Steiner Minimal Trees.
Suppose
In this paper, conditions under which the residual of
As a consequence, inequalities relating the sizes of smallest defining sets of
The exact sizes of smallest defining sets of
Exact designs with
On the contrary, in the case of negative autocorrelation, the minimum such number provides almost optimal designs. A list of the exact
A tree
The edges of the tree
Median graphs are surveyed from the point of view of their characterizations, their role in location theory, and their connections with median structures. The median structures we present include ternary algebras, betweenness, interval structures, semilattices, hypergraphs, join geometries, and conflict models. In addition, some new characterizations of median graphs as meshed graphs are presented and a new characterization in terms of location theory is given.
Up to isomorphisms, there are exactly 22
Let
If for any
In this paper, we first discuss some basic ideas used in proving interpolation theorems for graphs.
By using this, we then prove that a number of conditional invariants interpolate over some families of subgraphs of a given connected graph.
Scheduling graphs are used by algorithms such as PERT/CPM in order to determine an optimal schedule for a given project. It is well-known that dummy tasks (requiring zero processing time) must sometimes be incorporated into a scheduling graph.
The main tool in this paper is a new algorithm, RESOLVE, which creates a scheduling graph, typically with fewer dummy tasks than are produced by Richards’ algorithm (1967). A theoretical framework for scheduling graphs is systematically developed through several theorems, culminating in a demonstration of the validity of RESOLVE. A worked example illustrating the application of RESOLVE concludes the paper.
Let
From this result and some properties of intersection graphs on multifamilies, we determine the intersection numbers of
The concept of tenacity of a graph
Particular balanced bipartite subgraph problems have applications in fields such as VLSI design and flexible manufacturing. An example of such problems is the following: given a graph
We generalize the result to particular subclasses of
Using computer algorithms, we show that in any
Blocks of type
1970-2025 CP (Manitoba, Canada) unless otherwise stated.