Gromov hyperbolicity of Denjoy domains with hyperbolic and quasihyperbolic metrics

We obtain explicit and simple conditions which in many cases allow one decide, whether or not a Denjoy domain endowed with the Poincare or quasihyperbolic metric is Gromov hyperbolic. The criteria are based on the Euclidean size of the complement. Asa corollary, the main theorem allows to deduce the non-hyperbolicity of any periodic Denjoy domain.