Let A be known as a graph. By definition an independent set S is a group of vertices (could be 0 vertices, or could be all vertices) of A where there are no two vertices from S that are adjacent in graph A.
Let x(A) be the size of the greatest independent set of A. Let y(A) be the chromatic-# of graph A. If A has v vertices, please show that x(A)y(A)≥v.
Chromatic Number = The smallest # of colors that are required to color a graph.
The chromatic number gives us the number of independent sets. Let $I = \{ i : i$ is an independent set $\}$, and $x(A) = max \{ |i| : i \in I \}$. So we have $x(A)y(A) \geq y(A)\sum_{j=1}^{|I|} |i|$. By definition, $\sum_{j=1}^{I} |i| = V$. It follows that since $y(A) > 0$, $x(A)y(A) \geq V$.