My two cats are also fond of wrestling each other and chasing around the garden -this used to include up and down the trees but they've dropped this part as they've got older and fatter. They're both females, but next door lives a neutered tom called Monty. Each evening Monty strolls down our drive and sits around the back garden for a few minutes to show that he's the boss. My two ignore him and he ignores them. However, it's obviously important to Monty to carry out this daily ritual just to establish that our garden is also part of his territory. I suspect that if one of my cats was a tom, Monty's evening stroll wouldn't be quite so peaceful!