Write SQL query to solve given problem: List all the public institutes from the state with the least number of graduate cohort in 2013.. Keep the solution inside sql tag ```sql [SQL-Query] ```
SELECT T1.chronname FROM institution_details AS T1 INNER JOIN state_sector_grads AS T2 ON T1.state = T2.state WHERE T2.year = 2013 AND T1.control = 'Public' ORDER BY T2.grad_cohort LIMIT 1