no. 6
On r -hued coloring of product graphs
RAIRO. Operations Research, Tome 56 (2022) no. 6, pp. 3845-3852

A (k,r)-coloring of a graph G is a proper coloring with k colors such that for every vertex v with degree d(v) in G, the color number of the neighbors of v is at least min{d(v),r}. The smallest integer k such that G has a (k,r)-coloring is called the r-hued chromatic number and denoted by χ$$(G). In Kaliraj et al. [Taibah Univ. Sci. 14 (2020) 168–171], it is determined the 2-hued chromatic numbers of Cartesian product of complete graph and star graph. In this paper, we extend its result and determine the r-hued chromatic number of Cartesian product of complete graph and star graph.

DOI : 10.1051/ro/2022186
Classification : 05C15, 05C76
Keywords: ($$,$$)-coloring, $$-hued chromatic number, Cartesian product 
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Liang, Lingmei; Liu, Fengxia; Wu, Baoyindureng. On $r$-hued coloring of product graphs. RAIRO. Operations Research, Tome 56 (2022) no. 6, pp. 3845-3852. doi: 10.1051/ro/2022186

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