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Graphs: Problem 19 (1 point) Are the following statements true or false?

`◻`

1. Every graph has chromatic number 4 or less. 2. If

`\chi (G)=2`

, then

`G`

is a tree 3. If

`H`

is a subgraph of

`G`

, then

`\chi (H)=\chi (G)`

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4. If a graph contains a subgraph isomorphic to

`K_(10)`

, then the chromatic number of the graph is 10

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5. If a graph has a vertex of degree 3 , then the chromatic number must be at least 3 .