Togiri

Togiri is the het ship between Byakuya Togami and Kyouko Kirigiri from the Danganronpa fandom.

Canon
Byakuya and Kyouko do not have a good relationship. During their killing school life, Byakuya had always been suspicious of Kyouko, and even went as far as to taking her room key because she couldn't tell him what her reason for selection at Hope's Peak Academy was in chapter 5. Kyouko disliked him because of his lack of respect for human emotions, which she said would come back to bite him, with Byakuya shaking the remark off.

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 triump over despair.