Domination in Diameter-Two Graphs and the 2-Club Cluster Vertex Deletion Parameter

Faisal N. Abu-Khzam; Lucas Isenmann

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arXiv · 2408.08418

Domination in Diameter-Two Graphs and the 2-Club Cluster Vertex Deletion Parameter

Faisal N. Abu-Khzam·Lucas Isenmann

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Abstract

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.

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BibTeX RIS

Faisal N. Abu-Khzam, Lucas Isenmann. 2024-08-15. Domination in Diameter-Two Graphs and the 2-Club Cluster Vertex Deletion Parameter. https://arxiv.org/abs/2408.08418

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