Year: 2026
Type: preprint
Abstract: A set of vertices $S$ in a graph $G$ is a semitotal dominating set if $S$ is a dominating set and every vertex in $S$ has a witness, that is, another vertex in $S$ within distance at most two. The Semitotal Domination problem asks whether $G$ admits such a set of size at most $k$. We study this problem parameterized by the solution size. We provide a linear kernel of size $358k$ on planar graphs, a result that adds to several existing linear kernels for other domination variants on planar graphs. Additionally, we show Semitotal Domination is $W[2]$-hard on split graphs, on bipartite graphs and on $t$-claw-free graphs, it is $W[1]$-hard on circle graphs.
Source: arXiv (Cornell University)
Authors: de Lima, Paloma T., Retschmeier, Lukas
Institutions: Norwegian School of Economics, University of Copenhagen
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G5367877527
OpenAlex ID: W7224111132