A **critical graph** is a concept that can refer to multiple contexts in graph theory, but it is most commonly associated with two main definitions: 1. **In the context of graph coloring**: A critical graph is one that cannot be colored with a certain number of colors without violating the rules of proper coloring, and yet, by removing any one vertex, it becomes colorable with that number of colors. This means that a critical graph is "on the edge" of a particular coloring property.
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