Utilitas Algorithmica (UA)
ISSN: xxxx-xxxx (print)
Utilitas Algorithmica (UA) is a premier, open-access international journal dedicated to advancing algorithmic research and its applications. Launched to drive innovation in computer science, UA publishes high-impact theoretical and experimental papers addressing real-world computational challenges. The journal underscores the vital role of efficient algorithm design in navigating the growing complexity of modern applications. Spanning domains such as parallel computing, computational geometry, artificial intelligence, and data structures, UA is a leading venue for groundbreaking algorithmic studies.
- Research article
- Full Text
- Ars Combinatoria
- Volume 055
- Pages: 33-41
- Published: 30/04/2000
In this paper we determine the \(k\)-domination numbers of the cardinal products \(P_2 \times P_n, \ldots, P_{2k+1} \times P_n\) for all integers \(k \geq 2, n \geq 3\).
- Research article
- Full Text
- Ars Combinatoria
- Volume 055
- Pages: 25-31
- Published: 30/04/2000
In this paper we investigate the nature of both the \(2\)-packing number and the minimum domination number of the cartesian product of graphs where at least one of them has the property that every vertex is either a leaf or has at least one leaf as a neighbour.
- Research article
- Full Text
- Ars Combinatoria
- Volume 055
- Pages: 3-23
- Published: 30/04/2000
Let \(H\) be a graph, and let \(k\) be a positive integer. A graph \(G\) is \(H\)-coverable with overlap \(k\) if there is a covering of all the edges of \(G\) by copies of \(H\) such that no edge of \(G\) is covered more than \(k\) times. The number \(ol(H, G)\) is the minimum \(k\) for which \(G\) is \(H\)-coverable with overlap \(k\).
It is established (Theorem 2.1) that if \(n\) is sufficiently large then
\[ol(H, K_n) \leq 2.\]
For \(H\) being a path, a matching or a star it is enough to assume \(|H| \leq n\) (Theorem 3.1).
The same result is obtained (Main Theorem) for any graph \(H\) having at most four vertices, or else at most four edges with a single exception \(ol(K_4, K_5) = 3\).
- Research article
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 032
- Pages: 239-253
- Published: 29/02/2000
In this paper, we show that group divisible designs with block size five, group-type and index odd exist with a few possible exceptions.
- Research article
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 032
- Pages: 231-237
- Published: 29/02/2000
A digraph \(D\) is called semicomplete \(c\)-partite if its vertex set \(V(D)\) can be partitioned into \(c\) sets (partite sets) such that for any two vertices \(x\) and \(y\) in different partite sets, at least one arc between \(x\) and \(y\) is in \(D\) and there are no arcs between vertices in the same partite set. The path covering number of \(D\) is the minimum number of paths in \(D\) that are pairwise vertex disjoint and cover the vertices of \(D\). Volkmann (1996) has proved two sufficient conditions on hamiltonian paths in semicomplete multipartite digraphs and conjectured two related sufficient conditions. In this paper, we derive sufficient conditions for a semicomplete multipartite digraph to have path covering number at most \(k\) and show that Volkmann’s results and conjectures can be readily obtained from our conditions.
- Research article
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 032
- Pages: 223-229
- Published: 29/02/2000
The Fibonacci number of a graph is the number of independent sets of the graph. In this paper, we compute algorithmically the Fibonacci numbers of lattice product graphs.
- Research article
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 032
- Pages: 219-221
- Published: 29/02/2000
In this note, we solve a conjecture of Dénes, Mullen, and Suchower [2] on power sets of Latin squares.
- Research article
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 032
- Pages: 213-218
- Published: 29/02/2000
In this article, we construct a large set of idempotent quasigroups of order 62. The spectrum for large sets of idempotent quasigroups of order \(n\) (briefly, \(LQ(n)\)) is the set of all integers \(n \geq 3\) with the exception \(n = 6\) and the possible exception \(n = 14\).
- Research article
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 032
- Pages: 207-211
- Published: 29/02/2000
We settle the existence status of some previously open cases of abelian difference sets. Our results fill ten missing entries in the recent table of Lepez and Sanchez, all with answer `No’.
- Research article
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 032
- Pages: 203-206
- Published: 29/02/2000
Recently, Raines and Rodger have proved that for all \(\lambda \geq 1\), any partial extended triple system of order \(n\) and index \(\lambda\) can be embedded in a (complete) extended triple system of order \(v\) and index \(\lambda\) for any even \(v \geq 4n + 6\). In this note, it is shown that if \(\lambda\) is even then this bound on \(v\) can be improved to all \(v \geq 3n + 5\), and under some conditions to all \(v \geq 2n + 1\).
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