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Ch6 圖論
第 32 題／共 34 題
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LS 32/34
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32. Hamiltonian Graph、Eulerian Graph、Complete Bipartite Graph
#LS-06-032
中
Hamiltonian Graph
Eulerian Graph
Complete Bipartite Graph
📝
☆
Let
G
G
G
be a graph with at least three vertices.
A
If there is a Hamiltonian path between any two vertices of
G
G
G
,
G
G
G
must contain a Hamiltonian cycle.
B
If, at every vertex
v
v
v
in
G
G
G
, there is a Hamiltonian path which starts at
v
v
v
,
G
G
G
must contain a Hamiltonian cycle.
C
If there is an Eulerian trail (path) between any two vertices of
G
G
G
,
G
G
G
must contain an Eulerian circuit.
D
K
m
,
n
K_{m,n}
K
m
,
n
is Hamiltonian (a graph with a Hamiltonian cycle) if and only if
n
>
1
n > 1
n
>
1
and
m
=
n
m = n
m
=
n
.
E
K
m
,
n
K_{m,n}
K
m
,
n
is Eulerian (a graph with a Eulerian circuit) if and only if
m
m
m
and
n
n
n
are both odd.
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