
The graph resulting from contracting edge
We prove tight estimates on the minimum weight of an edge decomposition of the complete graph into subgraphs of 3 or 4 edges, where the weight of a subgraph is the number of its vertices. We conjecture that the weighted edge decomposition problem on general graphs is NP-complete for every
There are six distinct ways in which the vertices of a 4-cycle may be coloured with two colours, called \text{colouring types}. Let
For a solution
Approximately linear bounds are given for
Let
In this paper, we show the cordiality of the following families of graphs: (1) Pyramid graphs, (2) One point unions of plys,(3) One point unions of wheel related graphs, (4) Path unions of shells of different sizes, (5) Path unions of flags of different sizes.
Many different approaches exist in studying graphs with high connectivity and small diameter. We consider the effect of deleting vertices and edges from a graph while maintaining a small diameter. The following property is introduced: A graph
An
For two vertices
In recent work, Corteel and Lovejoy extensively studied overpartitions as a means of better understanding and interpreting various
and congruences such as
where
Let
We show that
If
We provide tables which summarize various aspects of the finite linear groups
It is conjectured that any 2-regular graph
1970-2025 CP (Manitoba, Canada) unless otherwise stated.