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arXiv · 2610.04917

W[1]-Hardness of Upper Clique Transversal

J. Pascal Gollin·Tesshu Hanaka·Ekkehard Köhler·Martin Milanič·Yushi Uno
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Abstract

A clique transversal of a graph is a set of vertices intersecting every maximal clique. We prove that deciding whether a graph has an inclusion-wise minimal clique transversal of size at least $k$ is W[1]-hard when parameterized by $k$.

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J. Pascal Gollin, Tesshu Hanaka, Ekkehard Köhler, Martin Milanič, Yushi Uno. 2026-10-10. W[1]-Hardness of Upper Clique Transversal. https://arxiv.org/abs/2610.04917

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