Planar graph or not (Kuratowski's Theorem)

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Graph planar or not



So the question is whether the graph given is planar or not. After some trial and error I think it is NOT planar, so I want to prove it using Kuratowski's Theorem but I couldn't break it down to $K_5$ or $K_3,3$. Would appreciate any help on this!



Also in general, is there any strategy that we can use when trying to apply Kuratowski's Theorem? Or any thing that can help to determine whether we should aim for $K_5$ or $K_3,3$? Or is it just purely trial and error? I got so frustrated when I could not figure it out.






discrete-mathematics graph-theory planar-graph







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  • What version of Kuratowski do you use: the one with minors? or subgraphs by subdivisions?
    – Henno Brandsma
    3 hours ago






  • 3




    There aren't too many points of degree 4, so I'd say go for $K_3,3$,
    – Henno Brandsma
    3 hours ago














up vote
1
down vote

favorite












Graph planar or not



So the question is whether the graph given is planar or not. After some trial and error I think it is NOT planar, so I want to prove it using Kuratowski's Theorem but I couldn't break it down to $K_5$ or $K_3,3$. Would appreciate any help on this!



Also in general, is there any strategy that we can use when trying to apply Kuratowski's Theorem? Or any thing that can help to determine whether we should aim for $K_5$ or $K_3,3$? Or is it just purely trial and error? I got so frustrated when I could not figure it out.






discrete-mathematics graph-theory planar-graph







share|cite|improve this question





















  • What version of Kuratowski do you use: the one with minors? or subgraphs by subdivisions?
    – Henno Brandsma
    3 hours ago






  • 3




    There aren't too many points of degree 4, so I'd say go for $K_3,3$,
    – Henno Brandsma
    3 hours ago












up vote
1
down vote

favorite









up vote
1
down vote

favorite











Graph planar or not



So the question is whether the graph given is planar or not. After some trial and error I think it is NOT planar, so I want to prove it using Kuratowski's Theorem but I couldn't break it down to $K_5$ or $K_3,3$. Would appreciate any help on this!



Also in general, is there any strategy that we can use when trying to apply Kuratowski's Theorem? Or any thing that can help to determine whether we should aim for $K_5$ or $K_3,3$? Or is it just purely trial and error? I got so frustrated when I could not figure it out.






discrete-mathematics graph-theory planar-graph







share|cite|improve this question













Graph planar or not



So the question is whether the graph given is planar or not. After some trial and error I think it is NOT planar, so I want to prove it using Kuratowski's Theorem but I couldn't break it down to $K_5$ or $K_3,3$. Would appreciate any help on this!



Also in general, is there any strategy that we can use when trying to apply Kuratowski's Theorem? Or any thing that can help to determine whether we should aim for $K_5$ or $K_3,3$? Or is it just purely trial and error? I got so frustrated when I could not figure it out.






discrete-mathematics graph-theory planar-graph




discrete-mathematics graph-theory planar-graph






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




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asked 3 hours ago









M. W

375




375











  • What version of Kuratowski do you use: the one with minors? or subgraphs by subdivisions?
    – Henno Brandsma
    3 hours ago






  • 3




    There aren't too many points of degree 4, so I'd say go for $K_3,3$,
    – Henno Brandsma
    3 hours ago
















  • What version of Kuratowski do you use: the one with minors? or subgraphs by subdivisions?
    – Henno Brandsma
    3 hours ago






  • 3




    There aren't too many points of degree 4, so I'd say go for $K_3,3$,
    – Henno Brandsma
    3 hours ago















What version of Kuratowski do you use: the one with minors? or subgraphs by subdivisions?
– Henno Brandsma
3 hours ago




What version of Kuratowski do you use: the one with minors? or subgraphs by subdivisions?
– Henno Brandsma
3 hours ago




3




3




There aren't too many points of degree 4, so I'd say go for $K_3,3$,
– Henno Brandsma
3 hours ago




There aren't too many points of degree 4, so I'd say go for $K_3,3$,
– Henno Brandsma
3 hours ago










1 Answer
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Remove the edge $BD$ and suppress vertices $B,D$. The original graph thus contains a subdivision of this resulting graph, which is isomorphic to $K_3,3$, so the original graph is not planar.






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  • Thanks for your answer!
    – M. W
    26 mins ago










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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
5
down vote



accepted










Remove the edge $BD$ and suppress vertices $B,D$. The original graph thus contains a subdivision of this resulting graph, which is isomorphic to $K_3,3$, so the original graph is not planar.






share|cite|improve this answer




















  • Thanks for your answer!
    – M. W
    26 mins ago














up vote
5
down vote



accepted










Remove the edge $BD$ and suppress vertices $B,D$. The original graph thus contains a subdivision of this resulting graph, which is isomorphic to $K_3,3$, so the original graph is not planar.






share|cite|improve this answer




















  • Thanks for your answer!
    – M. W
    26 mins ago












up vote
5
down vote



accepted







up vote
5
down vote



accepted






Remove the edge $BD$ and suppress vertices $B,D$. The original graph thus contains a subdivision of this resulting graph, which is isomorphic to $K_3,3$, so the original graph is not planar.






share|cite|improve this answer












Remove the edge $BD$ and suppress vertices $B,D$. The original graph thus contains a subdivision of this resulting graph, which is isomorphic to $K_3,3$, so the original graph is not planar.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered 3 hours ago









Parcly Taxel

37.6k137096




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  • Thanks for your answer!
    – M. W
    26 mins ago
















  • Thanks for your answer!
    – M. W
    26 mins ago















Thanks for your answer!
– M. W
26 mins ago




Thanks for your answer!
– M. W
26 mins ago

















 

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