The boxicity of a graph G is the least integer d such that G has an
intersection model of axis-aligned d-dimensional boxes. Boxicity, the problem
of deciding whether a given graph G has boxicity at most d, is NP-complete
for every fixed d≥2. We show that boxicity is fixed-parameter tractable
when parameterized by the cluster vertex deletion number of the input graph.
This generalizes the result of Adiga et al., that boxicity is fixed-parameter
tractable in the vertex cover number.
Moreover, we show that boxicity admits an additive 1-approximation when
parameterized by the pathwidth of the input graph.
Finally, we provide evidence in favor of a conjecture of Adiga et al. that
boxicity remains NP-complete when parameterized by the treewidth.Comment: 19 page