Most vets these days know that dogs like Greyhounds with little body fat need special anaesthetics when the have to have surgery, so this is not as much of a problem that it was a few years ago. However, it is still very worthwhile to make sure that your particular vet understands. Below is an article from Anne Finch's book, "Pet owners guide to the Greyhound". Page 64.
If your dog ever needs a general anaesthetic, make sure, tactfully, that your vet understands the special hazards of anaesthetising a dog with very little body fat, such as a Greyhound. Barbiturate, commonly used for inducing anaesthesia, can kill a Greyhound, as his lean body is unable to get rid of the drug, which keeps circulating round the system delaying his recovery. The dog may suffer a heart attack or never recover from the anaesthetic. Many vets nowadays use propofol or isoflurane for all their patients. These are safe for Greyhounds, but they are expensive. If your dog needs an anaesthetic for neutering or anything else, it is wise to have his teeth cleaned at the same time, which is good for your dog's health and your pocket in the long run.