Question

A tree is a connected graph that contains no cycles. Prove that any tree with two...

A tree is a connected graph that contains no cycles. Prove that any tree with two or more vertices has chromatic number 2.

Hi there! Please WRITE LEGIBLY and with clear steps. A lot of times I get confused by the solutions. Thank you!

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Answer #1

second method

Chose any vertices v in the given tree T. Let T be a rooted tree at vertex v.
suppose the first color is assigned to the root v. Paint all the vertices adjacent to v with
second color. Next paint the vertices adjacent to this using first color. Continue this
process till every vertex in T has been painted. Hence all the vertices at odd distance from
v have second color. While v and vertices at even distances from v have first color.

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