You can get some welded wire or chicken wire fencing and form it into a hoop house by anchoring the edges into the soil.
You can also make hoops from 1/2" PVC pipe and cover it with either wire or plastic fencing, bird netting etc.
That way the plants are protected from the sides and top.
Although the most budget friendly thing to do is nothing if you're cats aren't digging up the plants. Are they? I've never had an issue with cats digging up melons or any other plants for that matter.
Don't believe everything you see on the internet.
