
A twofold 8-cycle system is an edge-disjoint decomposition of a twofold complete graph (which has two edges between every pair of vertices) into 8-cycles. The order of the complete graph is also called the order of the 8-cycle system. A twofold 2-perfect
In this paper, we impose an extra condition on the twofold
We completely solve the existence of such twofold
We consider a storage/scheduling problem which, in addition to the standard restriction involving pairs of elements that cannot be placed together, considers pairs of elements that must be placed together. A set
Given a partition
An
A family
The metric dimension of some classes of convex polytopes has been determined in
In this paper, we study the metric dimension of an infinite class of convex polytopes which are obtained by the combinations of two different graphs of convex polytopes. It is shown that this infinite class of convex polytopes has constant metric dimension and only three vertices chosen appropriately suffice to resolve all the vertices of these classes of convex polytopes.
One natural extension of classical Ramsey numbers to multipartite graphs is to consider 2-colorings of the complete multipartite graph consisting of
By means of the
In [A.G. Chetwynd and A.J.W. Hilton, Critical star multigraphs, Graphs and Combinatorics 2 (1986), 209-221] Chetwynd and Hilton started the investigations of the edge-chromatic properties of a particular class of multigraphs, which they called star multigraphs. A star multigraph is a multigraph such that there exists a vertex
The main goal of this paper is to provide shorter and simpler proofs of all the main theorems contained in the above mentioned paper. Most simplifications are achieved by means of a formula for the chromatic index recently obtained by the author and by a careful use of arguments involving fans.
Broadcasting is the process of message transmission in a communication network. The communication network is modeled by a graph
A \textbf{k-port} line broadcasting in
In this paper, we extend Cohen’s work
In this paper we consider 1-movable dominating sets, motivated by the use of sensors employed to detect certain events in networks, where the sensors have a limited ability to react under changing conditions in the network. A 1-movable dominating set is a dominating set
A subset
Let
Let
A classic result is that every string
In 1983 J. P. Duval [6] published Algorithm 1, which finds
Since Duval used a programming language, we start by giving a new simple account of his Algorithm 1. Then our Algorithm 2 given here modifies Duval’s Algorithm 1 to find
Our Algorithm 3 is also for a string
We find interesting properties of Lyns, some of which may be new.
A family
The metric dimension of some classes of plane graphs has been determined in
The degree set of a graph
Let
The Stein-Lovasz Theorem can be used to get existence results for some combinatorial problems using constructive methods rather than probabilistic methods. In this paper, we discuss applications of the Stein-Lovasz Theorem to some combinatorial set systems and arrays, including perfect hash families, separating hash families, splitting systems, covering designs, lotto designs and
The distribution of distances in the star graph
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