In math, as in life, small choices can have big consequences. This is especially true in graph theory, a field that studies networks of objects and the connections between them. Here’s a little puzzle ...

When graph theorists label the vertices, they call it a “coloring.” A sudoku puzzle begins with a partial coloring, since only a few spots have numbers.

Assume we have a set of k colors and to each vertex of a graph G we assign an arbitrary subset of these colors. If we require that each vertex to which an empty set is assigned has in its neighborhood ...

Transactions of the American Mathematical Society, Vol. 311, No. 2 (Feb., 1989), pp. 697-710 (14 pages) By associating a collection of knots and links to a graph in three-dimensional space, we obtain ...