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changed question to 3-regular
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Bounds on the number of proper 3-colorings of (sub)cubiccubic graphs

Are there known bounds on the number of proper 3-colorings of a graph with maximum degree at most 3-regular in terms of vertex count?

Bounds on the number of proper 3-colorings of (sub)cubic graphs

Are there known bounds on the number of proper 3-colorings of a graph with maximum degree at most 3 in terms of vertex count?

Bounds on the number of proper 3-colorings of cubic graphs

Are there known bounds on the number of proper 3-colorings of a 3-regular in terms of vertex count?

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Bounds on the number of proper 3-colorings of (sub)cubic graphs

Are there known bounds on the number of proper 3-colorings of a graph with maximum degree at most 3 in terms of vertex count?