Key point 2.11 The standard Chinese postman problem starts and finishes at the same node. Sometimes a question will indicate that the route need not start and end at the same node. In this case, a semiEulerian network is needed, where the route will start at one odd-degree node and finish at another.
WORKED EXAMPLE 2.9
a Solve the problem in Worked example 2.8, but allowing the route to start and end at different nodes.
ii
D
iii
F
.
PL E
b Find how many times the route passes through i C
a The odd-degree nodes are A, B, D
and F .
One pair can remain odd, so you just need to find the shortest pairing of the other pair.
AB = 13, AD = 19, AF = 15 DF = 14, BF = 20, BD = 6
93 + 6 = 99 2
ii
2
iii
1
The route either starts or ends at F and also passes through F once.
M
b i
Route starts and ends at A and F , repeating BD .
SA
EXERCISE 2B 1
2
Classify each graph as Eulerian, semi-Eulerian or neither. A
B
C
D
The distance matrix for a network is shown.
Original material Š Cambridge University Press 2018