Now through Tuesday, the Westminster Kennel Club doggedly trots out its idea of purebred perfection. But as readers of The Post have proved for the last two years, a pup doesn’t need a pedigree to be top dog. This year’s no different, as dog lovers from as far away as Cheshire, England, wrote to tell us about the mutts — many of them rescues — who brighten their lives.  “She is definitely no pedigree,” writes Upper West Sider Joe Simon of his 5-year-old Chihuahua mix, Alice. “She is missing a few teeth and has an underbite, has lopsided ears and a tail that curls up like a piglet’s. This makes her all the more beautiful to us, and we wouldn’t have her any other way!”  Meet this year’s Best in Show, mixed-breed division: