Domination in Diameter-Two Graphs and the 2-Club Cluster Vertex Deletion Parameter
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910567632994304 |
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| author | Abu-Khzam, Faisal N. Isenmann, Lucas |
| author_facet | Abu-Khzam, Faisal N. Isenmann, Lucas |
| contents | The s-club cluster vertex deletion number of a graph, or sccvd, is the minimum number of vertices whose deletion results in a disjoint union of s-clubs, or graphs whose diameter is bounded above by s. We launch a study of several domination problems on diameter-two graphs, or 2-clubs, and study their parameterized complexity with respect to the 2ccvd number as main parameter. We further propose to explore the class of problems that become solvable in sub-exponential time when the running time is independent of some input parameter. Hardness of problems for this class depends on the Exponential-Time Hypothesis. We give examples of problems that are in the proposed class and problems that are hard for it. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_08418 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Domination in Diameter-Two Graphs and the 2-Club Cluster Vertex Deletion Parameter Abu-Khzam, Faisal N. Isenmann, Lucas Computational Complexity The s-club cluster vertex deletion number of a graph, or sccvd, is the minimum number of vertices whose deletion results in a disjoint union of s-clubs, or graphs whose diameter is bounded above by s. We launch a study of several domination problems on diameter-two graphs, or 2-clubs, and study their parameterized complexity with respect to the 2ccvd number as main parameter. We further propose to explore the class of problems that become solvable in sub-exponential time when the running time is independent of some input parameter. Hardness of problems for this class depends on the Exponential-Time Hypothesis. We give examples of problems that are in the proposed class and problems that are hard for it. |
| title | Domination in Diameter-Two Graphs and the 2-Club Cluster Vertex Deletion Parameter |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2408.08418 |