Gokudou Reijou, Neko wo Hirou.

One day, Akira, the granddaughter of the head of the Momiji gang, brings home a ragged young man named Nora who she finds collapsed in a garbage dump. At first, Nora shows a rebellious attitude, saying "I won't accept charity from the yakuza," but gradually he begins to call Akira "boss" and become attached to her... The story depicts the misunderstandings that surround Akira and Nora as they live together. (Source: Natalie, translated)