Answer: As you've discovered, cats love to dig in fresh soil. They will stop digging as soon as the grass is thick. The quickest and easiest way to keep cats from digging is to simply lay a piece of chicken wire over the reseeded area. The grass will grow through the holes and you can pick the wire up to mow the lawn, then replace it until the grass is nice and thick enough to keep the cats from digging. It won't blow away and it won't hurt if you or your dog walk on it.
Best wishes with your lawn!
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