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The chromatic polynomial of a graph G $G$ , denoted P ( G , m ) $P(G,m)$ , is equal to the number of proper m $m$ -colorings of G $G$ . The list color function of graph G $G$ , denoted P ℓ ( G , m ) ${P}_{\ell }(G,m)$ , is a list analogue of the chromatic polynomial that has been studied since the early 1990s, primarily through comparisons with the corresponding chromatic polynomial.
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