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Queue Layouts of Graphs with Bounded Degree and Bounded Genus (1901.05594v2)
Published 17 Jan 2019 in math.CO and cs.DM
Abstract: Motivated by the question of whether planar graphs have bounded queue-number, we prove that planar graphs with maximum degree $\Delta$ have queue-number $O(\Delta{2})$, which improves upon the best previous bound of $O(\Delta6)$. More generally, we prove that graphs with bounded degree and bounded Euler genus have bounded queue-number. In particular graphs with Euler genus $g$ and maximum degree $\Delta$ have queue-number $O(g+\Delta{2})$. As a byproduct we prove that if planar graphs have bounded queue-number, then graphs of Euler genus $g$ have queue-number $O(g)$.