Author

Michał Pilipczuk

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Preprint Sep 2026

SETH-based Lower Bound for Dynamic Degeneracy

It is proved that, unless SETH fails, for any $\varepsilon, \delta>0$, $k \in \mathbb{N}$, and function $f\colon \mathbb{N}\to \mathbb{N}$, there is no data structure which maintains a $(2-\varepsilon)-approximation of the degeneracy of $G$ with initialization time and amortized update time.

Konrad Majewski, Michał Pilipczuk · 0 citations

Jul 2026

Dynamic domination and independence in sparse graphs

It is proved that in graphs of degeneracy at most $d, one can maintain an ${cal O}(d^2)$-approximation of the minimum size of a (distance-$1) dominating set with amortized expected update time $d^{{\cal O}(1)}\cdot \log n$.

B. Bosek, Wojciech Nadara, Michał Pilipczuk et al. · arXiv.org · 0 citations