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Using this lower bound and two classical Ramsey-theoretic results from literature, we answer two questions posed by Milans, Stolee, and West [J. Combinatorics, 2015] (MSW15). First we show that the track number $\\tau(L(K_n))$ of the line graph of the complete graphs $K_n$ is at least $\\lg\\lg n - o(1)$. 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