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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 edge to a red edge, 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.