In this short note we give an elementary combinatorial argument, showing that the conjecture of J. Fernández de Bobadilla, I. Luengo-Velasco, A. Melle-Hernández and A. Némethi [Proc. London Math. Soc. 92 (2006), 99-138, Conjecture 1] follows from Theorem 5.4 of Brodzik and Livingston [arXiv:1304.1062] in the case of rational cuspidal curves with two critical points.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba62-2-2, author = {Piotr Nayar and Barbara Pilat}, title = {A Note on the Rational Cuspidal Curves}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, volume = {62}, year = {2014}, pages = {117-123}, zbl = {1307.14044}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba62-2-2} }
Piotr Nayar; Barbara Pilat. A Note on the Rational Cuspidal Curves. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 62 (2014) pp. 117-123. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba62-2-2/