Mixing
For what values of $n$ is the complete graph $K_n$ bipartite?
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 '18 at 14:51
Gaurang Tandon
3,51522148
asked Mar 5 '16 at 19:45
Tarek Nabulsi
163
add a comment |
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 '18 at 14:51
Gaurang Tandon
3,51522148
asked Mar 5 '16 at 19:45
Tarek Nabulsi
163
add a comment |
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 '18 at 14:51
Gaurang Tandon
3,51522148
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 '18 at 14:51
Gaurang Tandon
3,51522148
asked Mar 5 '16 at 19:45
Tarek Nabulsi
163
edited Nov 20 '18 at 14:51
Gaurang Tandon
3,51522148
asked Mar 5 '16 at 19:45
Tarek Nabulsi
163
edited Nov 20 '18 at 14:51
Gaurang Tandon
3,51522148
edited Nov 20 '18 at 14:51
Gaurang Tandon
3,51522148
edited Nov 20 '18 at 14:51
Gaurang Tandon
3,51522148
3,51522148
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
1
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HINT: A bipartite graph cannot contain a triangle.
answered Mar 5 '16 at 19:47
Brian M. Scott
455k38505907
add a comment |
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1 Answer
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1 Answer
1
active
oldest
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oldest
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active
oldest
votes
HINT: A bipartite graph cannot contain a triangle.
answered Mar 5 '16 at 19:47
Brian M. Scott
455k38505907
add a comment |
HINT: A bipartite graph cannot contain a triangle.
answered Mar 5 '16 at 19:47
Brian M. Scott
455k38505907
add a comment |
HINT: A bipartite graph cannot contain a triangle.
answered Mar 5 '16 at 19:47
Brian M. Scott
455k38505907
HINT: A bipartite graph cannot contain a triangle.
answered Mar 5 '16 at 19:47
Brian M. Scott
455k38505907
answered Mar 5 '16 at 19:47
Brian M. Scott
455k38505907
answered Mar 5 '16 at 19:47
Brian M. Scott
455k38505907
answered Mar 5 '16 at 19:47
Brian M. Scott
455k38505907
455k38505907
add a comment |
add a comment |
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