Solution-Prove that a tree with one vertex is bipartite

Prove that a tree with one vertex is bipartite

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Reference no: EM131173543

Recall that a graph is bipartite if and only if it is possible to colour the vertices with two colours, such that any two adjacent vertices have different colours. In this question, we will prove that all trees are bipartite by induction on the number of vertices.

(a) Prove that a tree with one vertex is bipartite.

(b) State the inductive hypothesis.

(d) Prove the inductive step. You may use the fact that every tree has a leaf (a vertex of degree 1).

Reference no: EM131173543

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Prove that a tree with one vertex is bipartite

Reference no: EM131173543

Reference no: EM131173543

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