Given a simple graph $G=(V,E)$, we use $A_k$ to denote the vertex set of a maximum $k$-colorable subgraph in $G$ when $k\ge 1$, and $A_0=0$.

Will the sequence $|A_1|-|A_0|,|A_2|-|A_1|,\cdots,|A_{\chi(G)}|-|A_{\chi(G)-1}|$ be a non-increasing sequence, where $\chi(G)$ denotes the chromatic number of graph $G$?