For each of the following statements, decide whether it is true or false. If it is true, include a (short, but clear) argument why it is true, and if it is false, include a concrete graph which shows that the claim is false. a) There is a tree which contains exactly one leaf. b) A graph can be colored with two colors if and only if it is bipartite. c) A graph on n ≥ 2 vertices with at most n − 2 edges is always acyclic

Database System Concepts
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ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
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For each of the following statements, decide whether it is true or false. If it is true, include a (short, but clear) argument why it is true, and if it is false, include a concrete graph which shows that the claim is false.

a) There is a tree which contains exactly one leaf.

b) A graph can be colored with two colors if and only if it is bipartite.

c) A graph on n ≥ 2 vertices with at most n − 2 edges is always acyclic. 

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