Year: 2026
Type: preprint
Abstract: We prove that every planar graph on $n$ vertices has a vertex ordering $v_1,v_2,\ldots,v_n$ in which each prefix $\{v_1,\ldots,v_i\}$ is joined to at most $C\sqrt{i}$ elements of $\{v_{i+1},\ldots,v_n\}$, where $C$ is an absolute constant. Consequently, every prefix can be separated from its complement by deleting $O\left(\sqrt{i}\right)$ vertices lying entirely in its complement.
Source: arXiv (Cornell University)
Authors: Mustafa, Nabil H., Pach, Janos
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223987040