Initially, Byakuya and Kyouko do not have a good relationship. During their killing school life, Byakuya had always been suspicious of Kyouko.
In Chapter 3 of Danganronpa 1, Byakuya is suspicious of Kyoko because of her sudden disappears during the time of both murders. In Chapter 4, Kyoko warns Byakuya that he shouldn't underestimate the others' emotions, as it may one day turn against him. At the time, Byakuya shakes the remark off. However, Kyoko's warning comes true later in the chapter when Byakuya is unable to figure out who the culprit was because he didn't take into consideration that Sakura could want to end her own life and that Aoi could act irrationally due to her friendship with Sakura. In Chapter 5, Byakuya goes as far as to taking Kyoko's room key because she couldn't tell him what her reason for selection at Hope's Peak Academy was.
Eventually, it seems they learned to work with each other during their time at the Future Foundation, possibly because they both had their memories returned. This can be seen that, despite his background and title, he is willing to be the vice head, working under Kyouko. When Kyouko was thought to have been killed during the Final Killing Game, Byakuya refers to her presumed death as a "great cost" for hope to finally triumph over despair.
The ship emerged as a result of Byakuya and Kyoko being two of the three main characters of Danganronpa 1, along with Makoto Naegi. Some fans prefer to ship them together due to both of them having a rather cold and cynical personality. Another similarity warmly welcomed by the fans includes both of them being the most useful characters during the investigations and Class Trials, aside from Makoto.
Some fan fictions tend to show them having crush on each other, despite their rather unfriendly beginnings during Killing School Life. Its main rival ships are Naegiri and Naegami, although some fans enjoy the dynamics between all three, resulting in Naegamigiri.
- Kyoko Kirigiri/Byakuya Togami tag on AO3
- Togami/Kirigiri tag on FanFiction.Net
- Byakuya/Kyoko tag on FanFiction.Net
- Byakuya's relationship with Kyoko on Danganronpa Wiki
- Kyoko's relationship with Byakuya on Danganronpa Wiki
- As shown in Future Arc, Kyoko is the acting head of Future Foundation's 14th division. While she's busy, Byakuya acts as the acting head of the division.