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How to generate random graphs free of certain structures?

Is it possible to generate random graphs free of certain forbidden structures? For example, graphs without $C_3$. If it is true, then it would be of great help in my research. Looking forward to all comments and suggestions.

How to generate random graphs free of certain structures?

Is it possible to generate random graphs free of certain forbidden structures? For example, graphs without $C_3$. $C_3$.

Or is it possible to test whether a graph is free of some forbidden structures?

If it is true, positive, then it would be of great help in my research. Looking forward to all comments and suggestions.