Describe all k-tuples (n1, n2,…,nk) of natural numbers, k = 1, 2,…, such that complete bipartite graph...
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I have tried this question by drawing different graphs and guessing but nothing general in is coming to be true for all complete bipartite graphs.
Question-
Describe all k-tuples $(n_1, n_2,...,n_k)$ of natural numbers, $k = 1, 2,...,$
such that complete bipartite graph $K(n_1,n_2,...,n_k)$ is a planar graph.
graph-theory
edited Nov 19 at 0:44
mathnoob
1,137116
asked Nov 18 at 12:10
Random
554
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up vote
0
down vote
favorite
I have tried this question by drawing different graphs and guessing but nothing general in is coming to be true for all complete bipartite graphs.
Question-
Describe all k-tuples $(n_1, n_2,...,n_k)$ of natural numbers, $k = 1, 2,...,$
such that complete bipartite graph $K(n_1,n_2,...,n_k)$ is a planar graph.
graph-theory
edited Nov 19 at 0:44
mathnoob
1,137116
asked Nov 18 at 12:10
Random
554
Do you know that every nonplanar graph contains either the complete graph on $5$ vertices $K_5$ or the complete bipartite graph on $6$ vertices $K_{3,3}$?
– M. Nestor
Nov 18 at 12:31
@M.Nestor No, is it necessarily true? And if it is true how do we say about k>2.
– Random
Nov 18 at 14:34
@M.Nestor Contains a subdivision of either $K_5$ or $K_{3,3}$, so it's not as straightforward as you make it sound.
– Misha Lavrov
Nov 18 at 16:12
What is a complete bipartite graph $K(n_1,...,n_k)$? Do yo mean complete multipartite graph?
– mathnoob
Nov 19 at 0:14
1
Here is a link about complete multipartite graph being planar :math.stackexchange.com/questions/256204/…
– mathnoob
Nov 19 at 0:21
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have tried this question by drawing different graphs and guessing but nothing general in is coming to be true for all complete bipartite graphs.
Question-
Describe all k-tuples $(n_1, n_2,...,n_k)$ of natural numbers, $k = 1, 2,...,$
such that complete bipartite graph $K(n_1,n_2,...,n_k)$ is a planar graph.
graph-theory
edited Nov 19 at 0:44
mathnoob
1,137116
asked Nov 18 at 12:10
Random
554
I have tried this question by drawing different graphs and guessing but nothing general in is coming to be true for all complete bipartite graphs.
Question-
Describe all k-tuples $(n_1, n_2,...,n_k)$ of natural numbers, $k = 1, 2,...,$
such that complete bipartite graph $K(n_1,n_2,...,n_k)$ is a planar graph.
graph-theory
graph-theory
edited Nov 19 at 0:44
mathnoob
1,137116
asked Nov 18 at 12:10
Random
554
edited Nov 19 at 0:44
mathnoob
1,137116
asked Nov 18 at 12:10
Random
554
edited Nov 19 at 0:44
mathnoob
1,137116
edited Nov 19 at 0:44
mathnoob
1,137116
edited Nov 19 at 0:44
mathnoob
1,137116
1,137116
asked Nov 18 at 12:10
Random
554
asked Nov 18 at 12:10
Random
554
asked Nov 18 at 12:10
Random
554
554
Do you know that every nonplanar graph contains either the complete graph on $5$ vertices $K_5$ or the complete bipartite graph on $6$ vertices $K_{3,3}$?
– M. Nestor
Nov 18 at 12:31
@M.Nestor No, is it necessarily true? And if it is true how do we say about k>2.
– Random
Nov 18 at 14:34
@M.Nestor Contains a subdivision of either $K_5$ or $K_{3,3}$, so it's not as straightforward as you make it sound.
– Misha Lavrov
Nov 18 at 16:12
What is a complete bipartite graph $K(n_1,...,n_k)$? Do yo mean complete multipartite graph?
– mathnoob
Nov 19 at 0:14
1
Here is a link about complete multipartite graph being planar :math.stackexchange.com/questions/256204/…
– mathnoob
Nov 19 at 0:21
add a comment |
Do you know that every nonplanar graph contains either the complete graph on $5$ vertices $K_5$ or the complete bipartite graph on $6$ vertices $K_{3,3}$?
– M. Nestor
Nov 18 at 12:31
@M.Nestor No, is it necessarily true? And if it is true how do we say about k>2.
– Random
Nov 18 at 14:34
@M.Nestor Contains a subdivision of either $K_5$ or $K_{3,3}$, so it's not as straightforward as you make it sound.
– Misha Lavrov
Nov 18 at 16:12
What is a complete bipartite graph $K(n_1,...,n_k)$? Do yo mean complete multipartite graph?
– mathnoob
Nov 19 at 0:14
1
Here is a link about complete multipartite graph being planar :math.stackexchange.com/questions/256204/…
– mathnoob
Nov 19 at 0:21
Do you know that every nonplanar graph contains either the complete graph on $5$ vertices $K_5$ or the complete bipartite graph on $6$ vertices $K_{3,3}$?
– M. Nestor
Nov 18 at 12:31
Do you know that every nonplanar graph contains either the complete graph on $5$ vertices $K_5$ or the complete bipartite graph on $6$ vertices $K_{3,3}$?
– M. Nestor
Nov 18 at 12:31
@M.Nestor No, is it necessarily true? And if it is true how do we say about k>2.
– Random
Nov 18 at 14:34
@M.Nestor No, is it necessarily true? And if it is true how do we say about k>2.
– Random
Nov 18 at 14:34
@M.Nestor Contains a subdivision of either $K_5$ or $K_{3,3}$, so it's not as straightforward as you make it sound.
– Misha Lavrov
Nov 18 at 16:12
@M.Nestor Contains a subdivision of either $K_5$ or $K_{3,3}$, so it's not as straightforward as you make it sound.
– Misha Lavrov
Nov 18 at 16:12
What is a complete bipartite graph $K(n_1,...,n_k)$? Do yo mean complete multipartite graph?
– mathnoob
Nov 19 at 0:14
What is a complete bipartite graph $K(n_1,...,n_k)$? Do yo mean complete multipartite graph?
– mathnoob
Nov 19 at 0:14
1
1
Here is a link about complete multipartite graph being planar :math.stackexchange.com/questions/256204/…
– mathnoob
Nov 19 at 0:21
Here is a link about complete multipartite graph being planar :math.stackexchange.com/questions/256204/…
– mathnoob
Nov 19 at 0:21
add a comment |
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Do you know that every nonplanar graph contains either the complete graph on $5$ vertices $K_5$ or the complete bipartite graph on $6$ vertices $K_{3,3}$?
– M. Nestor
Nov 18 at 12:31
@M.Nestor No, is it necessarily true? And if it is true how do we say about k>2.
– Random
Nov 18 at 14:34
@M.Nestor Contains a subdivision of either $K_5$ or $K_{3,3}$, so it's not as straightforward as you make it sound.
– Misha Lavrov
Nov 18 at 16:12
What is a complete bipartite graph $K(n_1,...,n_k)$? Do yo mean complete multipartite graph?
– mathnoob
Nov 19 at 0:14
1
Here is a link about complete multipartite graph being planar :math.stackexchange.com/questions/256204/…
– mathnoob
Nov 19 at 0:21