Geodesic
Colorings of the graph $K^m_2+K_n$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 3, pp. 297-305

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In this paper, we characterize chromatically unique, determine list-chromatic number and characterize uniquely list colorability of the graph $G=K^m_2+K_n$. We shall prove that $G$ is $\chi $-unique, $\mathrm{ch}(G)=m+n$, $G$ is uniquely $3$-list colorable graph if and only if $2m+n\geqslant 7$ and $m \geqslant 2$.
Keywords: chromatic number, list-chromatic number, chromatically unique graph, uniquely list colorable graph, complete $r$-partite graph. 
@article{JSFU_2020_13_3_a3,
     author = {Le Xuan Hung},
     title = {Colorings of the graph $K^m_2+K_n$},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {297--305},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_3_a3/}
}
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Le Xuan Hung. Colorings of the graph $K^m_2+K_n$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 3, pp. 297-305. http://geodesic.mathdoc.fr/item/JSFU_2020_13_3_a3/