How many matchings does a cycle on n vertices have?
0
$begingroup$
how many matchings does a cycle on n vertices have?
this is graph theory.
If n = 3, matching would be 3? and
If n = 4, matching should be 4 and
If n = 5, matching would be 10?
It seems there is no pattern
graph-theory matching-theory
asked Dec 7 '18 at 2:30
Jace ChoJace Cho
1
$endgroup$
add a comment |
0
$begingroup$
how many matchings does a cycle on n vertices have?
this is graph theory.
If n = 3, matching would be 3? and
If n = 4, matching should be 4 and
If n = 5, matching would be 10?
It seems there is no pattern
graph-theory matching-theory
asked Dec 7 '18 at 2:30
Jace ChoJace Cho
1
$endgroup$
1
$begingroup$
How do you get $4$ matchings for a cycle on $4$ vertices? I get $2$ matchings of size $2$, and $4$ matchings of size $1$, and . . . does the empty matching count? I get $7$ matchings, or $6$ nonempty matchings, or $2$ maximum matchings, or $2$ maximal matchings. How do you get $4$?
$endgroup$
– bof
Dec 7 '18 at 3:39
$begingroup$
My guess is that they want you to count all matchings of any size, including the empty matching. In that case there seems to be a nice pattern. I get $4$ matchings for $n=3$, $7$ matchings for $n=4$, $11$ matchings for $n=5$, ...
$endgroup$
– bof
Dec 7 '18 at 3:53
add a comment |
0
0
0
$begingroup$
how many matchings does a cycle on n vertices have?
this is graph theory.
If n = 3, matching would be 3? and
If n = 4, matching should be 4 and
If n = 5, matching would be 10?
It seems there is no pattern
graph-theory matching-theory
asked Dec 7 '18 at 2:30
Jace ChoJace Cho
1
$endgroup$
how many matchings does a cycle on n vertices have?
this is graph theory.
If n = 3, matching would be 3? and
If n = 4, matching should be 4 and
If n = 5, matching would be 10?
It seems there is no pattern
graph-theory matching-theory
graph-theory matching-theory
asked Dec 7 '18 at 2:30
Jace ChoJace Cho
1
asked Dec 7 '18 at 2:30
Jace ChoJace Cho
1
asked Dec 7 '18 at 2:30
Jace ChoJace Cho
1
asked Dec 7 '18 at 2:30
Jace ChoJace Cho
1
asked Dec 7 '18 at 2:30
Jace ChoJace Cho
1
1
1
$begingroup$
How do you get $4$ matchings for a cycle on $4$ vertices? I get $2$ matchings of size $2$, and $4$ matchings of size $1$, and . . . does the empty matching count? I get $7$ matchings, or $6$ nonempty matchings, or $2$ maximum matchings, or $2$ maximal matchings. How do you get $4$?
$endgroup$
– bof
Dec 7 '18 at 3:39
$begingroup$
My guess is that they want you to count all matchings of any size, including the empty matching. In that case there seems to be a nice pattern. I get $4$ matchings for $n=3$, $7$ matchings for $n=4$, $11$ matchings for $n=5$, ...
$endgroup$
– bof
Dec 7 '18 at 3:53
add a comment |
1
$begingroup$
How do you get $4$ matchings for a cycle on $4$ vertices? I get $2$ matchings of size $2$, and $4$ matchings of size $1$, and . . . does the empty matching count? I get $7$ matchings, or $6$ nonempty matchings, or $2$ maximum matchings, or $2$ maximal matchings. How do you get $4$?
$endgroup$
– bof
Dec 7 '18 at 3:39
$begingroup$
My guess is that they want you to count all matchings of any size, including the empty matching. In that case there seems to be a nice pattern. I get $4$ matchings for $n=3$, $7$ matchings for $n=4$, $11$ matchings for $n=5$, ...
$endgroup$
– bof
Dec 7 '18 at 3:53
1
1
$begingroup$
How do you get $4$ matchings for a cycle on $4$ vertices? I get $2$ matchings of size $2$, and $4$ matchings of size $1$, and . . . does the empty matching count? I get $7$ matchings, or $6$ nonempty matchings, or $2$ maximum matchings, or $2$ maximal matchings. How do you get $4$?
$endgroup$
– bof
Dec 7 '18 at 3:39
$begingroup$
How do you get $4$ matchings for a cycle on $4$ vertices? I get $2$ matchings of size $2$, and $4$ matchings of size $1$, and . . . does the empty matching count? I get $7$ matchings, or $6$ nonempty matchings, or $2$ maximum matchings, or $2$ maximal matchings. How do you get $4$?
$endgroup$
– bof
Dec 7 '18 at 3:39
$begingroup$
My guess is that they want you to count all matchings of any size, including the empty matching. In that case there seems to be a nice pattern. I get $4$ matchings for $n=3$, $7$ matchings for $n=4$, $11$ matchings for $n=5$, ...
$endgroup$
– bof
Dec 7 '18 at 3:53
$begingroup$
My guess is that they want you to count all matchings of any size, including the empty matching. In that case there seems to be a nice pattern. I get $4$ matchings for $n=3$, $7$ matchings for $n=4$, $11$ matchings for $n=5$, ...
$endgroup$
– bof
Dec 7 '18 at 3:53
add a comment |
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1
$begingroup$
How do you get $4$ matchings for a cycle on $4$ vertices? I get $2$ matchings of size $2$, and $4$ matchings of size $1$, and . . . does the empty matching count? I get $7$ matchings, or $6$ nonempty matchings, or $2$ maximum matchings, or $2$ maximal matchings. How do you get $4$?
$endgroup$
– bof
Dec 7 '18 at 3:39
$begingroup$
My guess is that they want you to count all matchings of any size, including the empty matching. In that case there seems to be a nice pattern. I get $4$ matchings for $n=3$, $7$ matchings for $n=4$, $11$ matchings for $n=5$, ...
$endgroup$
– bof
Dec 7 '18 at 3:53