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If possible let T+e1+e2+e2 be non planar
Then either one of e1, e2 or e3 or T must be in another plane
T is a tree of order atleast 4.
i.e maximum number of children per root is more than or equal to 4.
Hence vertices containing e1, e2, e3 have to be planar.
T being a tree with root is also in the same plane
Hence proved
Solution
If possible let T+e1+e2+e2 be non planar
Then either one of e1, e2 or e3 or T must be in another plane
T is a tree of order atleast 4.
i.e maximum number of children per root is more than or equal to 4.
Hence vertices containing e1, e2, e3 have to be planar.
T being a tree with root is also in the same plane
Hence proved

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  • 1. If possible let T+e1+e2+e2 be non planar Then either one of e1, e2 or e3 or T must be in another plane T is a tree of order atleast 4. i.e maximum number of children per root is more than or equal to 4. Hence vertices containing e1, e2, e3 have to be planar. T being a tree with root is also in the same plane Hence proved Solution If possible let T+e1+e2+e2 be non planar Then either one of e1, e2 or e3 or T must be in another plane T is a tree of order atleast 4. i.e maximum number of children per root is more than or equal to 4. Hence vertices containing e1, e2, e3 have to be planar. T being a tree with root is also in the same plane Hence proved