
Let
A bowtie is a simple graph on
We give a graph theoretic analogue of the celebrated Faber-Krahn inequality, that is, the first eigenvalue
The first eigenvalue
The edge-reduction of a simple regular graph is an operation which removes two vertices and preserves the regularity. It has played an important role in the study of cubic graphs
[6,7,8]. Our main purpose is to study the structure of edge-irreducible quartic graphs. All edge-irreducible quartic graphs are determined from a constructive viewpoint. Then, a
unique decomposition theorem for edge-irreducible quartic graphs is obtained.
In this paper, we employ the structures of a permutation graph as exhibited in the Euclidean representation to solve the existence and construction problems of Hamiltonian cycles on permutation graphs. We define and prove the existence of a layered Hamiltonian cycle in a Hamiltonian permutation graph. A linear (in size) time and (in order) space algorithm for construction of a layered Hamiltonian cycle on a permutation graph is presented and its
correctness proven.
Cyclotomy can be used to construct a variety of combinatorial designs, for example, supplementary difference sets, weighing matrices, and
With the help of computer algorithms, we improve the upper bound on the classical three-color Ramsey number
is
We also present computer enumeration of all
Conjecture 119 in the file “Written on the Wall”, which contains the output of the computer program “Graffiti” of Fajtlowicz, states: If
Theorem. Let
In this paper, we derive some inequalities on the existence of two-symbol balanced arrays (B-arrays) of strength five. We then apply these inequalities to obtain an upper bound on the number of constraints for these arrays, and provide an illustrative example.
A graph
Let
In this paper, we prove that the Equitable
An array
We study two-dimensional pattern matching, and several other related problems, all of which depend on finding the period of an array.
In summary, finding the period of an array in parallel using
In [5] Kløve gave tables of the best bounds known on the size of optimal difference triangle sets. In this note, we give examples of difference triangle sets found by computer search which improve on the upper bounds in [5]. In four cases, these examples are proved to be optimal.
A Latin square
Such a Latin square is said to be \emph{holy}
Let
We show that, for any
Let
We prove that a
The main object of this paper is the construction of BIBD’s with
We have carried out a large number of computer searches for the base sequences
and we also investigate the borderline case
1970-2025 CP (Manitoba, Canada) unless otherwise stated.