A subcubic planar graph is a planar graph whose vertices have degree at most three. We show that the subcubic planar graphs with at least five vertices have planar slope number at most four, which is worst case optimal. This answers an open question by Jelínek et al. [6]. As a corollary, we prove that the subcubic planar graphs with at least five vertices have angular resolution π/4, which solves an open problem by Kant [7] and by Formann et al. [4].
The planar slope number of subcubic graphs
DI GIACOMO, Emilio;LIOTTA, Giuseppe;MONTECCHIANI, FABRIZIO
2014
Abstract
A subcubic planar graph is a planar graph whose vertices have degree at most three. We show that the subcubic planar graphs with at least five vertices have planar slope number at most four, which is worst case optimal. This answers an open question by Jelínek et al. [6]. As a corollary, we prove that the subcubic planar graphs with at least five vertices have angular resolution π/4, which solves an open problem by Kant [7] and by Formann et al. [4].File in questo prodotto:
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