Let $G$ be a simple, finite, undirected graph with vertex set $\left\{v_{1}, \ldots, v_{n}\right\}$. Let $\Delta(G)$ denote the maximum degree of $G$ and let $\mathbb{N}=\{1,2, \ldots\}$ denote the set of all possible colors. Color the vertices of $G$ using the following greedy strategy: for $i=1, \ldots, n$
$\operatorname{color}\left(v_{i}\right) \leftarrow \min \left\{j \in \mathbb{N}\right.$ : no neighbour of $v_{i}$ is colored $\left.j\right\}$
Which of the following statements is/are $\text{TRUE}?$
- This procedure results in a proper vertex coloring of $G$.
- The number of colors used is at most $\Delta(G)+1$.
- The number of colors used is at most $\Delta(G)$.
- The number of colors used is equal to the chromatic number of $G$.