Radius, girth and minimum degree

The objective of the present paper is to study maximum radius r a connected graph order n, minimum degree δ ≥ 2 and girth at least g 4. Erdős, Pach, Pollack Tuza proved that if = 4, is, triangle-free, then ≤ n − + 12, noted up value additive constant, this upper bound tight. In we shall determine exact maximum. For larger values little known. We settle for 6 , 8 prove an every even g, which conjecture be tight constant factor. Finally, show our implies so-called Erdős conjecture.