
For integers
In this paper, we solve the existence problem for covering the
The general linear group
A
In this paper, we show that this conjecture is completely false. Namely, for each integer
Let
The rainbow Ramsey number
A set
We use exhaustive computer searches to show that there are exactly
The minimum number of blocks having maximum size precisely four that are required to cover, exactly
Among the well-studied maximal planar graphs, those having the maximum possible number of 3-cycles are precisely the planar chordal graphs (meaning no induced cycles of lengths greater than three). This motivates a somewhat similar result connecting maximal planar bipartite graphs, 4-cycles, and planar chordal bipartite graphs (meaning bipartite with no induced cycles of lengths greater than four), together with characterizations of planar chordal bipartite graphs as radial graphs of outerplanar multigraphs.
Combinatorial designs are a powerful tool because of their beautiful combinatorial structure that can help in many applications, such as coding theory or cryptography. A conference key distribution system is a scheme to design a conference key, and then to distribute this key to only participants attending the conference in order to communicate with each other securely. In this paper, we present an efficient conference key distribution system using difference families. Using techniques for creating the conference key and for performing authentication based on identification information, the communication protocol is designed. Applying the known results on difference families, we obtain many new infinite classes of conference key distribution systems. In special classes of difference families, the message overhead is
In this paper, finite
We establish that for each of the 5005 possible types of 2-factorizations of the complete graph
Scheduling static tasks on parallel architectures is a basic problem arising in the design of parallel algorithms. This NP-complete problem has been widely investigated in the literature and remains one of the most challenging questions in the field. Among the resolution methods for this type of problems, the taboo search technique is of particular interest. Based on this technique, two algorithms are proposed and tested on a sample of instances in order to be compared experimentally with other well-known algorithms. The results clearly indicate good overall performances of our algorithms. Next, some NP-completeness results are established showing that this problem is intractable for approximation, even for some restricted cases bearing a clear relation to the instances treated experimentally in this work.
A graph
In this paper we generalize a result of Hakimi and Schmeichel in several ways. First to
We consider labeling edges of graphs with elements from abelian groups. Particular attention is given to graphs where the labels on any two Hamiltonian cycles sum to the same value. We find several characterizations for such labelings for cubes, complete graphs, and complete bipartite graphs. This extends work of [1, 8, 9, 10]. We also consider the computational complexity of testing if a labeled graph has this property and show it is NP-complete even when restricted to integer labelings of 3-connected, cubic, planar graphs with face girth at least five.
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