[Definition] The martingale collar is a collar that has only a section on it that will tighten when pulled. It consists of the main collar piece, as well as a smaller chain or fabric loop where the leash attached. While they are now mainly used as a training collar, they were originally called Greyhound collars and used on breeds such as Sighthounds whose necks are as big around as their heads and can easily slip out of a flat buckle collar. The chain loop allows the collar to be loose and comfortable, but tightens if the dog attempts to back out of it. [Tool] 
Martingale collar
T r a i n i n g c o l l a r
P r o n g c o l l a r o r p i n c h c o l l a r
R a d i o - c o n t r o l l e d c o l l a r s
M a r t i n g a l e c o l l a r
H e a d c o l l a r
N o - p u l l h a r n e s s
D o g b i t e t u g