
Let
If an edge-disjoint decomposition of a complete graph of order
(1) in each of the three pairings, there exists a metamorphosis into a
We show that such a complete set of metamorphoses from paired
Let
A dominating set is a vertex subset
Let
In [1], we showed that for
A Costas Latin square of order
Let
A Roman dominating function on a graph
We show that if
Let
A subset
Clatworthy described the eleven group divisible designs with three groups, block size four, and replication number at most 10. With these in mind one might ask: Can each of these designs be generalized in natural ways? In two previous papers the existence of natural generalizations of four of these designs were settled. Here we essentially settle the existence of natural generalizations of five of the remaining seven Clatworthy designs.
A complete solution is obtained for the possible number of common entries between two Latin squares of different given orders. This intersection problem assumes the entries of the smaller square are also entries of the larger, and that, for comparison, the smaller square is overlayed on the larger. However, these extra restrictions do not affect the solution, apart from one small example.
Let
It has been known for some time that the Higman-Sims graph can be decomposed into the disjoint union of two Hoffman-Singleton graphs. In this paper, we establish that the Higman-Sims graph can be edge decomposed into the disjoint union of 5 double-Petersen graphs, each on 20 vertices. It is shown that, in fact, this can be achieved in 36,960 distinct ways. It is also shown that these different ways fall into a single orbit under the automorphism group
Recently, Graves, Pisanski, and Watkins have determined the growth rates of Bilinski diagrams of one-ended, 3-connected, edge-transitive planar maps. The computation depends solely on the edge-symbol
We give general lower bounds and upper bounds on the maximum degree
We simplify and further develop the methods and ideas of [A. Gagarin, W. Kocay, “Embedding graphs containing
A graph
A difference system of sets (DSS) is a collection of subsets of
We give a new proof of the sufficiency of Landau’s conditions for a non-decreasing sequence of integers to be the score sequence of a tournament. The proof involves jumping down a total order on sequences satisfying Landau’s conditions and provides a
For graphs
In this paper, we look at families
A graph is singular if the zero eigenvalue is in the spectrum of its
A decycling set in a graph
We prove that the complete graph
Global routing in VLSI (very large scale integration) design is one of the most challenging discrete optimization problems in computational theory and practice. In this paper, we present a polynomial time algorithm for the global routing problem based on integer programming formulation with a theoretical approximation bound. The algorithm ensures that all routing demands are satisfied concurrently, and the overall cost is approximately minimized.
We provide both serial and parallel implementation as well as develop several heuristics used to improve the quality of the solution and reduce running time. We provide computational results on two sets of well-known benchmarks and show that, with a certain set of heuristics, our new algorithms perform extremely well compared with other integer-programming models.
In 1956, Ryser gave a necessary and sufficient condition for a partial Latin rectangle to be completable to a Latin square. In 1990, Hilton and Johnson showed that Ryser’s condition could be reformulated in terms of Hall’s Condition for partial Latin squares. Thus, Ryser’s Theorem can be interpreted as saying that any partial Latin rectangle
We define Hall’s Condition for partial Sudoku squares and show that Hall’s Condition for partial Sudoku squares gives a criterion for the completion of partial Sudoku rectangles that is both necessary and sufficient. In the particular case where
Let
Let
Let
In this paper, we consider three local convexity properties with respect to
Let
1970-2025 CP (Manitoba, Canada) unless otherwise stated.