Martingale Collars are important. Italian Greyhounds are sighthounds, and are very visually reactive with a top speed of 35 mph. They are NOT safe off-leash except in a fully fenced area. When outside a fenced area, an IG MUST be on a martingale collar and leash at all times. A properly fitted martingale collar prevents an IG (with their neck the same size as their head) from slipping out and escaping, as happens with a regular buckle collar.
Martingale collars can be purchased online. Below are two recommended sites: