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Graphs
are vertices connected together by edges.

Graph theory is an important part of mathematics
and graphs are often used to represent things in computer science.

For example, you could use vertices to represent cities, and
edges to represent flights between cities.

Coloring a graph is assigning a color to each edge or vertex.

Each level in the later sections has rules about which colors
can connect to which and which colors edges can be.

You can press R to see those rules.

A white edge or vertex represents "any color" and a gray
vertex represents "the same color". For example, this:

Means you can't create any edges between vertices of the same color.
For example, you can't connect a red vertex to a red vertex, regardless
of the edge color.

There are also rules which enforce a minimum or maximum number of
edges or vertices of some color. For example,

means that the maximum number of green edges is 3.

If the edge or vertex is gray, it means that the maximum or minimum
is for all colors, so you can't have more than some number of vertices or edges of any specific
color.

If the edge or vertex is white, that restricts the *total* number of vertices.