Queue Layouts of Graphs with Bounded Degree and Bounded Genus

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 $O({\Delta }^6)$. 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 $O(g)$.

Cited by in corpus (1)

• Separating layered treewidth and row treewidth