In SQL, is it OK for two tables to refer to each other?

No, it’s not OK. Circular references between tables are messy. See this (decade old) article: SQL By Design: The Circular Reference

Some DBMS can handle these, and with special care, but MySQL will have issues.

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Option 1

As your design, to make one of the two FKs nullable. This allows you to solve the chicken-and-egg problem (which table should I first Insert into?).

There is a problem though with your code. It will allow a product to have a default picture where that picture will be referencing another product!

To disallow such an error, your FK constraint should be:

CONSTRAINT FK_products_1 
  FOREIGN KEY (id, default_picture_id) 
  REFERENCES products_pictures (product_id, id)
  ON DELETE RESTRICT                            --- the SET NULL options would 
  ON UPDATE RESTRICT                            --- lead to other issues

This will require a UNIQUE constraint/index in table products_pictures on (product_id, id) for the above FK to be defined and work properly.

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Option 2

Another approach is to remove the Default_Picture_ID column form the product table and add an IsDefault BIT column in the picture table. The problem with this solution is how to allow only one picture per product to have that bit on and all others to have it off. In SQL-Server (and I think in Postgres) this can be done with a partial index:

CREATE UNIQUE INDEX is_DefaultPicture 
  ON products_pictures (Product_ID)
  WHERE IsDefault = 1 ;

But MySQL has no such feature.

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Option 3

This approach, allows you to even have both FK columns defined as NOT NULL is to use deferrable constraints. This works in PostgreSQL and I think in Oracle. Check this question and the answer by @Erwin: Complex foreign key constraint in SQLAlchemy (the All key columns NOT NULL Part).

Constraints in MySQL cannot be deferrable.

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Option 4

The approach (which I find cleanest) is to remove the Default_Picture_ID column and add another table. No circular path in the FK constraints and all FK columns will be NOT NULL with this solution:

product_default_picture
----------------------
product_id          NOT NULL
default_picture_id  NOT NULL
PRIMARY KEY (product_id)
FOREIGN KEY (product_id, default_picture_id)
  REFERENCES products_pictures (product_id, id)

This will also require a UNIQUE constraint/index in table products_pictures on (product_id, id) as in solution 1.

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To summarize, with MySQL you have two options:

• option 1 (a nullable FK column) with the correction above to enforce integrity correctly

• option 4 (no nullable FK columns)