Geodesic
On chromatic uniqueness of some complete tripartite graphs
Ural mathematical journal, Tome 7 (2021) no. 1, pp. 38-65

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Let $P(G, x)$ be a chromatic polynomial of a graph $G$. Two graphs $G$ and $H$ are called chromatically equivalent iff $P(G, x) = H(G, x)$. A graph $G$ is called chromatically unique if $G\simeq H$ for every $H$ chromatically equivalent to $G$. In this paper, the chromatic uniqueness of complete tripartite graphs $K(n_1, n_2, n_3)$ is proved for $n_1 \geqslant n_2 \geqslant n_3 \geqslant 2$ and $n_1 - n_3 \leqslant 5$.
Keywords: chromatic uniqueness, chromatic equivalence, complete multipartite graphs, chromatic polynomial. 
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     author = {Pavel A. Gein},
     title = {On chromatic uniqueness of some complete tripartite graphs},
     journal = {Ural mathematical journal},
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     publisher = {mathdoc},
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     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2021_7_1_a3/}
}
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Pavel A. Gein. On chromatic uniqueness of some complete tripartite graphs. Ural mathematical journal, Tome 7 (2021) no. 1, pp. 38-65. http://geodesic.mathdoc.fr/item/UMJ_2021_7_1_a3/