Not only must they be purebred but must be registered with the AKC and have their AKC papers.
There is no needed rule by the AKC regarding how a breeder breeds their dogs, such as line breeding, out crossing or in breeding. Read The Bible and the good Lord had a lot of close close line breeding going on back in the day. It would take up pages & more pages to explain the genetics of all of this but ethical dog breeders try to breed correctly such as line breeding and others do in breeding. You just really need to know what you are doing to do in breeding. You will find out your dogs' faults and good points in a hurry when in breeding. Done correctly, in breeding will bring out the best things in your dogs, once you have gotten rid of the bad genes. I am putting this very simply here. I don't even know why this was brought up here, has nothing to do with the question asked.
The purpose of being a show dog is being a purebred dog. You are showing your dog at a licensed AKC dog show which is judged by Judges who have been in the dog world a long time and are experienced in knowing the type & correct conformation of each breed they are allowed to judge. The purpose of this is to show that your dog meets all the standards set forth by that Breeds' Parent Club for the correct conformation in that particular breed. The idea being that the superior dog will become a Champion of record and an inferior dog would never become a Champion. That is how it is suppose to work but there are certain flaws in every sport.
2nd Answer:
Unfortunately The last time I checked the AKC did not have a rule regarding In-breeding or Line-breeding. Many breeders do this so when you look at those AKC (worthless ) papers it looks like there is a lot of champions in your dogs background.
Many dog breeders have been caught for obtaining AKC papers by using a dead dogs papers. Many more breeders have not been caught.
All purebred dogs.
Yes, variations in coat color in purebred dogs can result from dominant and recessive genes. Dominant genes can override recessive genes to produce certain coat colors, resulting in the observed variations in purebred dogs.
It depends on the specific breed.
poodle
Crossed or Mutts
A purebred short can be about a variety of different animals. Usually purebred shorts describe dogs or cats and their breeds.
The Kennel Club
No, but the puppies will me mixed, not purebred.
nothing, dogs not purebred, it can't be bred to make a purebred, its worthless.
Purebred dogs are more expensive due to the cost of breeding, genetic testing, health screenings, and meeting breed standards. Additionally, purebred dogs often come from reputable breeders who invest time, effort, and resources into producing quality puppies with desirable traits and characteristics.
A purebred Great Dane.
A show dog is a dog of very high quality and is a purebred.