Which is the minimum number of days that are required,so that all the exams are taken? In a university, the secretariat plans the examination period. There are $6$ subjects, $A,B,C,D,E,Z$ and $9$ students($1, \dots , 9$). At the subject $A$ the students $1,2,3$ are subscribed, at the subject $B$ the students $1,2,9$, at the subject $C$ the students $1,7,8$, at the subject $D$ the students $3,5,7,9$, at the subject $E$ the students $4,5,8$ and at the subject $Z$ the students $4,6,8$. Each examination lasts $2$ hours, and it can only be during the morning hours $10-12$. The only restriction at the planning is that it is not allowed that $2$ subjects, ,at which the same student is subscribed , get examinated simultaneously.
Which is the minimum number of days that are required,so that all the exams are taken?
I tried to solve the exerise,with the chromatic number,using the following graph:

So,the minimum number of days is $4$..or am I wrong??

I added labels to the graph's edges, for anyone having trouble seeing what's going on.

In addition, here is a table of the classes and students.
$$
\newcommand{\x}{\blacksquare}
\begin{array}{|c|cccccc|}
\hline
    &  A  &  B  &  C  &  D  &  E  &  Z  \\
\hline
1   & \x  & \x  & \x  &     &     &     \\
2   & \x  & \x  &     &     &     &     \\
3   & \x  &     &     & \x  &     &     \\
4   &     &     &     &     & \x  & \x  \\
5   &     &     &     & \x  & \x  &     \\
6   &     &     &     &     &     & \x  \\
7   &     &     & \x  & \x  &     &     \\
8   &     &     & \x  &     & \x  & \x  \\
9   &     & \x  &     & \x  &     &     \\
\hline
\end{array}
$$
