When directory 'a' does NOT exist:
$ strace mkdir -p ./a/b/c
mkdir("a", 0775) = 0
open("a", O_RDONLY|O_NOCTTY|O_NONBLOCK|O_DIRECTORY|O_NOFOLLOW) = 3
fchdir(3) = 0
close(3) = 0
mkdir("b", 0775) = 0
open("b", O_RDONLY|O_NOCTTY|O_NONBLOCK|O_DIRECTORY|O_NOFOLLOW) = 3