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AustraliaVIC
VCE 12 General 2023

9.04 Bipartite networks

Interactive practice questions

The principal of a school wants to allocate 3 teachers to 3 classes. The following bipartite graph shows all possible allocations of the teachers.

If each teacher can only take one class, which of the following allocations are possible? Select all the correct options.

Teacher Class
$T_1$T1 $C_1$C1
$T_2$T2 $C_2$C2
$T_3$T3 $C_3$C3
A
Teacher Class
$T_1$T1 $C_2$C2
$T_2$T2 $C_1$C1
$T_3$T3 $C_3$C3
B
Teacher Class
$T_1$T1 $C_3$C3
$T_2$T2 $C_2$C2
$T_3$T3 $C_1$C1
C
Teacher Class
$T_1$T1 $C_1$C1
$T_2$T2 $C_3$C3
$T_3$T3 $C_2$C2
D
Easy
1min

Consider the following bipartite graph.

Easy
< 1min

Consider the following bipartite graph.

Easy
< 1min

Which of the following bipartite graphs represent the given reduced table?

Easy
1min
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Outcomes

U4.AoS2.6

construct a transition matrix from a transition diagram or a written description and vice versa

U4.AoS2.13

recognise the matching problem and solve it by inspection or using the Hungarian algorithm for larger scale problems

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