Year: 2026
Type: preprint
Abstract: We prove that the domination number of the $2$-token graph of the path $P_n$ is $γ(F_2(P_n))=d(n)$ for every $n\ge 13$, where $d(n)=\frac1{10}(n^2+5n+c)$ and $c$ is an explicit constant that depends on $n \bmod 5$. This settles a conjecture by Leaños and the authors, who previously proved the upper bound. The lower bound is computer-assisted and follows the method used by Gonçalves, Pinlou, Rao and Thomassé for grid graphs.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221129609