In this note, we consider rational cuspidal plane curves having exactly one cusp whose complements have logarithmic Kodaira dimension two. We classify such curves with the property that the strict transforms of them via the minimal embedded resolution of the cusp have the maximal self-intersection number. We show that the curves given by the classification coincide with those constructed by Orevkov.
"On Orevkov's rational cuspidal plane curves." J. Math. Soc. Japan 64 (2) 365 - 385, April, 2012. https://doi.org/10.2969/jmsj/06420365