I am divorced. My daughter is a full time college student. Her father and I share her college expenses. We also alternate years when we claim her as a dependent. This is his year to do so. Are there any deductions related to her tuition that I can claim?

No, unfortunately you can only deduct the tuition if you are claiming your daughter as a dependent.

Who Can Claim the Deduction

Generally, you can claim the tuition and fees deduction if all three of the following requirements are met.

1. You pay qualified education expenses of higher education.
2. You pay the education expenses for an eligible student.
3. The eligible student is yourself, your spouse, or your dependent for whom you claim an exemption on your tax return.

See Publication 970 for more info:

Publication 970 (2007), Tax Benefits for Education

Agreed!