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Let Pm Pn be the strong product of two paths Pm and Pn. In 2013, Klešč et al. conjectured that the crossing number of Pm Pn is equal to (m − 1)(n − 1) − 4 for m ≥ 4 and n ≥ 4. In this paper we show that the above conjecture is true except when m = 4 and n = 4, and that the crossing number of P4 P4 is four.
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