If you were to boil it down to the absolute nessesities of marriage... it would be:
-man
-woman
-God
-Marriage covenant
-God's act of making the man and woman one
the verse goes "what God has joined together let no one seperate" not "what the state of so-and-so has joined together let no one seperate"
(Matt 19:6)
If you need more than that... what did Adam & Eve do?
It is best to have witnesses and the whole deal. Marriage is a celebration of life and God's promise, and should be treated that way.