
We modify the Knuth-Klingsberg Gray code for unrestricted integer compositions to obtain a Gray code for integer compositions each of whose parts is bounded between zero and some positive integer. We also generalize Ehrlich’s method for loop-free sequencing to implement this Gray code in
The following problem was introduced at a conference in 1995. Fires start at
In this paper, we are concerned with the existence of sets of mutually quasi-orthogonal Latin squares (MQOLS). We establish a correspondence between equidistant permutation arrays and MQOLS, which has facilitated a computer search to identify all sets of MQOLS of order
For a countable bounded principal ideal poset
A vertex set
We introduce a new class of colorings of graphs and define and study two new graph coloring parameters. A \emph{coloring} of a graph
This paper revises Park’s proof of Shannon inequality and also gives a new simple proof.
For
For a graph
Corresponding to chessboards, we introduce game boards with triangles or hexagons as cells and chess-like pieces for these boards. The independence number
We study the discrepancies of set systems whose incidence matrices are encoded by binary strings which are complex in the sense of Kolmogorov-Chaitin. We show that these systems display an optimal degree of irregularity of distribution.
We use the idea of compressibility to examine the discrepancy of set systems coded by complex sequences.
A multigraph is irregular if no two of its vertices have the same degree. It is known that every graph
Furthermore, these bounds are shown to be sharp.
The conjecture by E. Wojcicka, that every 3-domination-critical graph with minimum degree at least two is hamiltonian, has recently been proved in three different papers by five different authors. We survey the results which lead to the proof of the conjecture and consolidate them to form a unit.
The inflated graph
This paper considers the following question: how many non-isomorphic proper edge-colourings (with any number of colours) are there of the complete graph
A directed network connecting a set
Existence in the undirected case was first shown by E. J. Cockayne [Canad. Math. Bull. 10 (1967) 431-450].
A graph
In this study, we consider the effect on the upper irredundance number
A graph
We prove some general results on irredundant sets of queens on chessboards, and determine the irredundance numbers of the queens graph
Let
For
1970-2025 CP (Manitoba, Canada) unless otherwise stated.