Succah 3:3

If the aravos (the willow) are stolen or dried up, they are invalid. If they came from an asheirah (a tree worshipped as an idol) or a condemned city, they are invalid. If the tip broke off or the leaves separated, or if they were from a tzaftzafah (a certain species of willow), they are invalid. If they shriveled, some leaves fell off, or they came from a field, they are valid.

Succah 3:4

Rabbi Yishmael says that a person must wave three hadassim (myrtle), two aravos (willow), one lulav (palm branch) and one esrog (citron), even if two of the hadassim are broken; Rabbi Tarfon says even if all three are broken. Rabbi Akiva says that just as one only needs a single lulav and a single esrog, so too he only needs one hadas and one aravah.