MHB How many hours are needed for team meetings?

[evinda]

Hello! :)

I am looking at this exercise:

We have these teams : $E_{1},E_{2},...,E_{6}$ . Each team must have a meeting.
How many hours are needed (minimum) so that all the meetings take part, given that:

$$ E_{1}=\{A,B,C\} $$
$$ E_{2}=\{A,D,E\} $$
$$ E_{3}=\{B,C,Z\} $$
$$ E_{4}=\{Z,H,T\} $$
$$ E_{5}=\{E,H\} $$
$$ E_{6}=\{D,E,T\} $$

?

I tried to answer the question with this graph:

View attachment 2545

So, $3$ hours are needed,so that all the meetings take part...
Is it right or have I done something wrong? (Blush)

 

[caffeinemachine]

Hello! :)

I am looking at this exercise:

We have these teams : $E_{1},E_{2},...,E_{6}$ . Each team must have a meeting.
How many hours are needed (minimum) so that all the meetings have been done, given that:

$$ E_{1}=\{A,B,C\} $$
$$ E_{2}=\{A,D,E\} $$
$$ E_{3}=\{B,C,Z\} $$
$$ E_{4}=\{Z,H,T\} $$
$$ E_{5}=\{E,H\} $$
$$ E_{6}=\{D,E,T\} $$

?

I tried to answer the question with this graph:

https://www.physicsforums.com/attachments/2545

So, $3$ hours are needed,so that all the meetings take part...
Is it right or have I done something wrong? (Blush)

Looks right to me. You found out the chromatic number of the graph. Nice!

 

[evinda]

Looks right to me. You found out the chromatic number of the graph. Nice!

Great! (Clapping) Thank you! :)