re: What college football conferences have permanent cross divisional rivals?

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The Pac-12 does. Standford and Cal always play USC and UCLA

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This.

The Cali schools refused to be in separate divisions unless they played each other every year.

A lot of it is pure tradition as they're the oldest rivals in the conference.

And a lot of it is recruiting.

Cal and Stanford didn't want to be playing in Los Angeles once every couple of years.