Finding Euler Circuits and
Path so far: FEACBD.
A
C
EF
d Paths
B
D
F
Finding Euler Circuits and
Path so far: FEACBD. Don’t
A
C
EF
d Paths
cross the bridge!
B
D
F
Finding Euler Circuits and
Path so far: FEACBDC
A
C
EF
d Paths
B
D
F
Finding Euler Circuits and
Path so far: FEACBDC Now w
A
C
EF
d Paths
we have to cross the bridge CF.
B
D
F
Finding Euler Circuits and
Path so far: FEACBDCF
A
C
EF
d Paths
B
D
F
Finding Euler Circuits and
Path so far: FEACBDCFD
A
C
EF
d Paths
B
D
F
Finding Euler Circuits and
Path so far: FEACBDCFDB
A
C
EF
d Paths
B
D
F
Finding Euler Circuits and
Euler Path: FEACBDCFDBA
A
C
EF
d Paths
A
B
D
F
Finding Euler Circuits and
Euler Path: FEACBDCFDBA
A
C
EF
d Paths
A
B
D
F
Fleury’s Algorithm
To find an Euler path or an
Euler circuit:
Fleury’s Algorithm
To find an Euler path or an
1. Make sure the graph has e
Euler circuit:
either 0 or 2 odd vertices.
Fleury’s Algorithm
To find an Euler path or an
1. Make sure the graph has e
2. If there are 0 odd vertices,
odd vertices, start at one o
Euler circuit:
either 0 or 2 odd vertices.
start anywhere. If there are 2
of them.
Fleury’s Algorithm
To find an Euler path or an
1. Make sure the graph has e
2. If there are 0 odd vertices,
odd vertices, start at one o
3. Follow edges one at a time
a bridge and a non-bridge,
Euler circuit:
either 0 or 2 odd vertices.
start anywhere. If there are 2
of them.
e. If you have a choice between
always choose the non-bridge.
Fleury’s Algorithm
To find an Euler path or an
1. Make sure the graph has e
2. If there are 0 odd vertices,
odd vertices, start at one o
3. Follow edges one at a time
a bridge and a non-bridge,
4. Stop when you run out of e
Euler circuit:
either 0 or 2 odd vertices.
start anywhere. If there are 2
of them.
e. If you have a choice between
always choose the non-bridge.
edges.
Fleury’s Algorithm
To find an Euler path or an
1. Make sure the graph has e
2. If there are 0 odd vertices,
odd vertices, start at one o
3. Follow edges one at a time
a bridge and a non-bridge,
4. Stop when you run out of e
This is called Fleury’s algorith
Euler circuit:
either 0 or 2 odd vertices.
start anywhere. If there are 2
of them.
e. If you have a choice between
always choose the non-bridge.
edges.
hm, and it always works!
Fleury’s Algorithm: Anoth
AB
EF
JK
O
N
her Example
CD
GH
LM
PQ
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Euler Paths and Euler Circuits ... The Handshaking Theorem The Handshaking Theorem says that In every graph, the sum of the degrees of all vertices
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