Drawing subcubic planar graphs with four slopes and optimal angular resolution

A subcubic planar graph is a planar graph whose vertices have degree at most 3. We show that the subcubic planar graphs with at least five vertices have planar slope number at most 4, which is worst-case optimal. This answers an open question by Jelínek et al. [10]. Furthermore, we prove that the subcubic planar graphs with at least five vertices have angular resolution π/4, which solves an open problem by Kant [11] and by Formann et al. [8].