Genosai

SaiGenos is the slash ship between Saitama and Genos from the One-Punch Man fandom.

Canon
Saitama and Genos first met when Genos was fighting against Mosquito Girl. Genos notices Saitama standing idly nearby and warns him to leave as it is dangerous, before continuing his fight, when he blasted away an attack from the monster, however, the heat and power from the counterattack was so strong that it burned away all of Saitama's cloths, leaving him naked. Saitama doesn't seem too concerned about his lack of coverage and instead comments that Genos "really saved him" and that he's quite amazing right before Mosquito Girl reappears and attacks Genos. She injures Genos enough that he almost self-destructs, but doesn't, because Saitama steps in.

Genos watched as Saitama defeated the monster with one slap, he was in awe of his power and asked for Saitama to take him in as his disciple, which Saitama agrees, not taking Genos seriously.

A week later, Genos shows up at Saitama's doorstep. Saitama is annoyed and wants Genos to leave, but Genos is persistent and ends up telling Saitama his entire life story, which Saitama has made clear he has no interest in listening. Genos credits Saitama for saving him and keeps talking until Saitama snaps at him in annoyance to shorten whatever he's saying.

Genos does shorten it, and Saitama agrees to take Genos as his disciple seriously this time. They are interrupted when some monsters from the House of Evolution burst through Saitama's ceiling. Genos goes to take out the two outside but Saitama does it before he can. More monsters appear, when Saitama is faced with of the monsters while seemingly helpless, Genos is concerned and is momentarily distracted from his battle with Armored Gorilla, they both end up defeating their respective opponents and head towards the House of Evolution.

While Saitama was annoyed by his new disciple at first, he gradually warmed up to him. He also hold respect for Genos as he's an S-Class Hero and also his overall abilities. Saitama doesn't seem too worried about Genos' body safety though, as he's almost completely destroyed in every fight. Even though that is the case, Saitama still takes care of him should be torn to shreds or just saves him from complete destruction.

They're currently roommates and officially teacher and disciple, even though that mostly comes from Genos' side. However, Saitama often gives good advice to him.

Questionable Canonity
While this is not definitive proof that the author intended for Saitama and Genos to be canon, the ED for the first season of One Punch Man, "Hoshi Yori Saki Ni" by Hiroko Moriguchi, has lyrics that some would claim seem like something Genos would sing, and it's a love song. Also the ED for the second season, "Chizu ga Nakutemo Modoru kara" by Makoto Furukawa (the voice actor of Saitama in the Japanese dub), has lyrics that are speculated by some to be a reply to the first ED. Regardless of whether this has anything to do with canon, the shipping community does take inspiration from these songs in their fanwork.

Fanon
Their alternate ship name "EggToaster" or "Egg x Toaster" comes from Saitama's egg-shaped head and Genos' arms, which has vents that somewhat resemble a toaster's slots.

In the fandom, the ship is usually a bromance or platonic, but because there is still a decent about of SaiGenos shippers who ship it romantically, the term is usually referring to the romantic pairing. In fanworks they are often depicted in a domestic lifestyle, often making fun of Saitama's penny-pinching tendencies. Fans have also noticed how Genos rarely shows his emotions or anger unless Saitama is involved, usually when someone insults or "endangers" his master.

SaiGenos is the most popular and one of the oldest ships in the One Punch Man fandom, as well as the most written ship for the fandom on AO3.

Fandom
FAN FICTION
 * Saitama/Genos tag on FanFiction.Net
 * Saitama/Genos tag on FanFiction.Net

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Trivia

 * Genos is notably one of the only people Saitama seems to genuinely care about, Genos is also one of the few people who knows of Saitama's strength and became his friend.