0 a diagram consisting of a line or lines drawn to show changes in some quantity -- graf
a graph of temperature changes.
The properties of such graphs in which is much smaller than d have been studied extensively.
Here we will need a slight extension of that result, assuming that only two out of the three bipartite graphs are -regular.
The example in the immediately preceding paragraph shows that such graphs exist.
However, this is not possible in the unimodular case of unweighted graphs.
In many instances (such as undirected graphs and other symmetric relations) this is also a natural definition of a subobject.
We introduce new operations, particular for the class of graphs with path-width at most two.
The class of graphs with tree-width at most three requires four excluded minors [1].
The second theme is to illustrate the use of induction in proving such results about graphs and matroids.
