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arXiv · 2607.19134

Parameterized Complexity of Odd Domination and its Generalization

Toranosuke Kokai·Rin Saito·Tatsuhiro Suga·Takahiro Suzuki·Yuma Tamura
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Abstract

In the \textsc{Odd Domination} problem, given a graph $G$ and a positive integer $k$, the task is to determine whether there exists a vertex subset $D$ of $G$ such that the closed neighborhood of each vertex in $G$ contains an odd number of vertices from $D$. In this paper, we investigate the computational complexity of the problem. When parameterized by the solution size $k$, we establish W[1]-hardness on some restricted graphs and a sharp boundary between fixed-parameter tractability and W[1]-hardness with respect to the girth of the input graph. Then, we address the problem when parameterized by several structural graph parameters. Furthermore, we investigate the parameterized complexity of \textsc{Parity Domination}, which is a generalization of \textsc{Odd Domination}.

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Toranosuke Kokai, Rin Saito, Tatsuhiro Suga, Takahiro Suzuki, Yuma Tamura. 2026-07-21. Parameterized Complexity of Odd Domination and its Generalization. https://arxiv.org/abs/2607.19134

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