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In particular, Hoppen and Wormald showed in 2015 that $i(3, \\infty) \\ge 0.4375$, and Cs\\'oka improved it to $i(3,\\infty) \\ge 0.44533$ in 2016. Bollob\\'as proved the upper bound $i(3,\\infty) < \\frac{6}{13}$ in 1981, and McKay improved it to $i(3,\\infty) < 0.45537$ in 1987. 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Recently, several new lower bounds of $i(3,\\infty)$ were obtained. In particular, Hoppen and Wormald showed in 2015 that $i(3, \\infty) \\ge 0.4375$, and Cs\\'oka improved it to $i(3,\\infty) \\ge 0.44533$ in 2016. Bollob\\'as proved the upper bound $i(3,\\infty) < \\frac{6}{13}$ in 1981, and McKay improved it to $i(3,\\infty) < 0.45537$ in 1987. 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