Question

Write a nice proof of the fact that every tree is planar

Answer 1

Explanation:

Proof. We will use induction on the number of vertices p = |V |. Base Case: For p = 1, the only trees with one vertex have no edges, that is, q = 0, and clearly any such tree is planar. Inductive Step: Assume that for some p ≥ 1, all trees with p vertices are planar.

hope you get it now....

Answer 2

Explanation:

If T = (V,E) is a tree with p = |V | vertices and q = |E| edges, then T is a planar graph. Proof. ... We will show that this implies that any tree with p + 1 vertices is planar. Let T = (V,E) be a tree with |V | = p + 1 vertices and |E| = |V | − 1 edges.