½ ! " # $%
&'(# )
*
+ # + ,- .) ,-
$%
&/(# 0 0 ) 1 &2( 3 3 1 )
" # + + 1 ,-
4.) ½ # ½ +
+ 5 .) # + + 5 # + 5 + + 5
# + + +
5 #
+ # 5 + 5
# + +6 7 / 7 8 / + * 5
/ + ) 1 .) " ) +
) .
+ 7 8 / 8 / * # 3 3 ) + . 1 .
7 / 3
# 3 ) +
9
0 / + This edge may or may not belong
to a matching if x_i is true.
It cannot be part of the matching if
x_i is false
C1
Clauses that
contain X_i
K(d(C1, x1)) = {0,1}
S(C1, x1)
There must be 0 or 1
edge ajacent to this
node in the matching.
C2
K(d(C2, x1)) = {0,1}
S(C2, x1)
Belongs to the
matching if X_i
is true
T
K(x_i) = {0,3}
X_i
Belongs to the
matching if X_i
is false
F
K(~x_i) = {0,3}
All or no
edges must be
matched to
these nodes
S(C3, ~x1)
C3
Clauses that
contain ~X_i
K(d(C3, ~x1)) = {0,1}
S(C4, ~x1)
K(d(C4, ~x1)) = {0,1}
C4
Edges connected to nodes
d(C4, x_i) for i > 1
. .) # + .) : 0 ' 0 /
1 5 # + 5 # + )
0 ' ) 0 4 + ,-
,-
) + ; ; 3 0%1:
1 ); ;
+ &7 /(
!
" #
$%&'$%(
& )* #
&+,'&-
$ ) . /0 1 2*3
* 4 )
0 / 1 5Æ
/ ) ,
#
&++$
6 #
7
8 9
/ ) ,
#
&++$