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In this paper, we investigate for a given triple $(a,b,c)$ of positive integers whether there exists a graph $G$ such that $\\omega(G) = a$, $\\chi(G) = b$, and $\\chi_{\\rho}(G) = c$. If so, we say that $(a, b, c)$ is realizable. It is proved that $b=c\\ge 3$ implies $a=b$, and that triples $(2,k,k+1)$ and $(2,k,k+2)$ are not realizable as soon as $k\\ge 4$. 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Rall, Kirsti Wash, Sandi Klav\\v{z}ar","submitted_at":"2017-07-16T16:55:16Z","abstract_excerpt":"The packing chromatic number $\\chi_{\\rho}(G)$ of a graph $G$ is the smallest integer $k$ such that the vertex set of $G$ can be partitioned into sets $V_i$, $i\\in [k]$, where each $V_i$ is an $i$-packing. In this paper, we investigate for a given triple $(a,b,c)$ of positive integers whether there exists a graph $G$ such that $\\omega(G) = a$, $\\chi(G) = b$, and $\\chi_{\\rho}(G) = c$. If so, we say that $(a, b, c)$ is realizable. It is proved that $b=c\\ge 3$ implies $a=b$, and that triples $(2,k,k+1)$ and $(2,k,k+2)$ are not realizable as soon as $k\\ge 4$. 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