Year: 2026
Type: preprint
Abstract: For planar graphs, it is known that their treewidth is bounded by $O(\sqrt{n})$, where $n$ is the number of vertices of the graph. A related invariant to treewidth, is the scramble number of graphs. Recently, Connor et. al proved that planar graphs of bounded maximal degree have scramble number bounded by $O(\sqrt{n})$. An open question is whether the scramble number of any planar graph follows this same bound. We give a definitive answer with an explicit bound for a subset of planar graphs, the simple outerplanar graphs and the simple near outerplanar graphs.
Source: arXiv (Cornell University)
Author: Laboy, Doel Rivera
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208749604