We determine the thickness of the Cartesian product K₆ₚ₊₄ \, \, P₂ for p ≥ 0 and of the Cartesian product K₈ \, \, Pₘ for m ≥ 1 , where Kₙ and Pₘ denote the complete graph on n vertices and the path on m vertices, respectively. These are two of the three remaining cases from the results of Chen, Kohonen, and Yang [6]. Combined with their results, the thickness of Kₙ \, \, P₂ is completely determined.
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Kenta Noguchi (2026) studied this question.
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