For what values of $n$ is the complete graph $K_n$ bipartite?
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I understand what complete graphs are and what bipartite graphs are. In the bipartite graph, every point from the same set is not connected, but they are connected to every other point of the other set. But my question is, but what values of $n$ in $K_n$ is $K$ bipartite?
I think that the best way to answer this question is $K_{m,n}$ where $m$ are vertices in one partition and $n$ are vertices in another partition. I'm not sure if there is another way to look at this though.
discrete-mathematics
edited Nov 20 at 14:51
Gaurang Tandon
3,48522147
asked Mar 5 '16 at 19:45
Tarek Nabulsi
163
add a comment |
up vote
1
down vote
favorite
I understand what complete graphs are and what bipartite graphs are. In the bipartite graph, every point from the same set is not connected, but they are connected to every other point of the other set. But my question is, but what values of $n$ in $K_n$ is $K$ bipartite?
I think that the best way to answer this question is $K_{m,n}$ where $m$ are vertices in one partition and $n$ are vertices in another partition. I'm not sure if there is another way to look at this though.
discrete-mathematics
edited Nov 20 at 14:51
Gaurang Tandon
3,48522147
asked Mar 5 '16 at 19:45
Tarek Nabulsi
163
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I understand what complete graphs are and what bipartite graphs are. In the bipartite graph, every point from the same set is not connected, but they are connected to every other point of the other set. But my question is, but what values of $n$ in $K_n$ is $K$ bipartite?
I think that the best way to answer this question is $K_{m,n}$ where $m$ are vertices in one partition and $n$ are vertices in another partition. I'm not sure if there is another way to look at this though.
discrete-mathematics
edited Nov 20 at 14:51
Gaurang Tandon
3,48522147
asked Mar 5 '16 at 19:45
Tarek Nabulsi
163
I understand what complete graphs are and what bipartite graphs are. In the bipartite graph, every point from the same set is not connected, but they are connected to every other point of the other set. But my question is, but what values of $n$ in $K_n$ is $K$ bipartite?
I think that the best way to answer this question is $K_{m,n}$ where $m$ are vertices in one partition and $n$ are vertices in another partition. I'm not sure if there is another way to look at this though.
discrete-mathematics
discrete-mathematics
edited Nov 20 at 14:51
Gaurang Tandon
3,48522147
asked Mar 5 '16 at 19:45
Tarek Nabulsi
163
edited Nov 20 at 14:51
Gaurang Tandon
3,48522147
asked Mar 5 '16 at 19:45
Tarek Nabulsi
163
edited Nov 20 at 14:51
Gaurang Tandon
3,48522147
edited Nov 20 at 14:51
Gaurang Tandon
3,48522147
edited Nov 20 at 14:51
Gaurang Tandon
3,48522147
3,48522147
asked Mar 5 '16 at 19:45
Tarek Nabulsi
163
asked Mar 5 '16 at 19:45
Tarek Nabulsi
163
asked Mar 5 '16 at 19:45
Tarek Nabulsi
163
163
add a comment |
add a comment |
1 Answer
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up vote
3
down vote
HINT: A bipartite graph cannot contain a triangle.
answered Mar 5 '16 at 19:47
Brian M. Scott
454k38504906
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
HINT: A bipartite graph cannot contain a triangle.
answered Mar 5 '16 at 19:47
Brian M. Scott
454k38504906
add a comment |
up vote
3
down vote
HINT: A bipartite graph cannot contain a triangle.
answered Mar 5 '16 at 19:47
Brian M. Scott
454k38504906
add a comment |
up vote
3
down vote
up vote
3
down vote
HINT: A bipartite graph cannot contain a triangle.
answered Mar 5 '16 at 19:47
Brian M. Scott
454k38504906
HINT: A bipartite graph cannot contain a triangle.
answered Mar 5 '16 at 19:47
Brian M. Scott
454k38504906
answered Mar 5 '16 at 19:47
Brian M. Scott
454k38504906
answered Mar 5 '16 at 19:47
Brian M. Scott
454k38504906
answered Mar 5 '16 at 19:47
Brian M. Scott
454k38504906
454k38504906
add a comment |
add a comment |
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