Johnny Carson (1925-2005) was an American TV presenter, comedian and the host of "The Tonight Show" from 1962 until 1992.
Zappa was a guest in Carson's show during the April 3, 1986 broadcast.  Carson is one of the people receiving thanks for their "very special but no less significant contributions" in The Yellow Shark liner notes.
References in Zappa's music
Johnny Carson is mentioned in Zappa's song Magdalena in the line: "My God, I was only following the sexual impulse like I heard on the Johnny Carson Show from a book or something I wrote."
Zappa about Carson
Zappa: "I thought Johnny Carson was a nice guy to talk with, and he surprised me when I went on the show because when I was brought on I was told that we were only going to talk about Miami Vice. He didn't want to talk about politics or anything else. He surprised everybody by talking about censorship, and he told me before the show that he had stayed up -- you know those Senate hearings when they were broadcast live, they didn't broadcast them completely. Just before I went on to testify they switched to the Senate floor. Consequently they reran the whole thing on Saturday and Sunday at two o'clock in the morning. Johnny Carson said that he stayed up and watched them. Which also surprised me, the idea that Johnny Carson sits around watching C-span on the weekends is pretty fascinating."
R&RD: Speaking for myself, I was extremely annoyed that Carson relegated you to the last five minutes of the show in that Phantom Zone where they put anyone with opinions.
Zappa: "That’s true on every talk show."
R&RD: But they had some lady with an egg collection who went on and on and on. She took up nearly the whole show.
Zappa: "Want to know the story about the egg lady?" (...) She had a vision that she was going to be on Johnny Carson and she called them. And it was so off the wall. She called them from some kind of phone booth in a shopping mall in New Jersey or something like that and they said, “Oh this has got to be great.” And they brought her out just because she got in contact with them. It was just off the wall, and it didn’t turn out to be quite as good as they thought it was going to be. And they devoted this major segment of the show to it."
R&RD: Which I thought was a big mistake.
Zappa: "Well don’t tell me, tell them."