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  "path": "/abs/2603.14749v1",
  "publishedAt": "2026-03-17T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Jiayi Zheng",
    "Boning Meng"
  ],
  "textContent": "**Authors:** Jiayi Zheng, Boning Meng\n\nWe introduce a new framework of counting problems called #GDS that encompasses #$(σ, ρ)$-Set, a class of domination-type problems that includes counting dominating sets and counting total dominating sets. We explore the intricate relation between #GDS and the well-known Holant. We propose the technique of gadget construction under the #GDS framework; using this technique, we prove the #P-completeness of counting dominating sets for 3-regular planar bipartite simple graphs. Through a generalization of a Holant dichotomy, and a special reduction method via symmetric bipartite graphs, we also prove the #P-completeness of counting total dominating sets for the same graph class.",
  "title": "The Counting General Dominating Set Framework"
}