Definition 3
Given a graph G(V, E),
a cut
C
=
(S, V-S) is a
partition of vertex set V into two subsets, S and V-S such that
every vertex must belong to either S or V-S, but not both.
Definition 4
Given a cut
C
= (S, V-S), an edge (
u
,
v
) is said
to
cross
the cut if
u
∈
S and
v
∈
V-S.
Definition 5
Given a set A of edges, a cut
C
= (S, V-S) is said
to respect
the set A if no edges in A crosses the cut.
Definition 6
Given a cut
C
, an edge is called
a light edge
crossing the cut if its weight is the minimum among all crossing
edges.
Example 2
b
h
a
i
g
c
d
e
f
4
11
8
8
7
7
1
2
6
2
14
9
10
4
S
V-S
S = {
a
,
b
,
d
,
e
}
V - S = {
c
,
f
,
g
,
h
,
i
}
A = {(
a
,
b
),
(
i
,
c
), (
c
,
f
), (
f
,
g
), (
g
,
h
)}
(bold edges)
Crossing edges
= {(
a
,
h
),
(
b
,
h
), (
b
,
c
), (
d
,
c
), (
d
,
f
), (
e
,
f
)}
Light edge
= (
d
,
c
),
w
(
d
,
c
) = 7.
Fig. 23-2