Marcin Pilipczuk

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20242026

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cs.DM2025

A polynomial bound on the number of minimal separators and potential maximal cliques in $P_{6}$ -free graphs of bounded clique number

Marcin Pilipczuk, PaweÅ RzÄ Å¼ewski

In this note we show a polynomial bound on the number of minimal separators and potential maximal cliques in $P_{6}$ -free graphs of bounded clique number.

cs.DM2024

Bounding $ε$ -scatter dimension via metric sparsity

Romain Bourneuf, Marcin Pilipczuk

A recent work of Abbasi et al. [FOCS 2023] introduced the notion of $ε$ -scatter dimension of a metric space and showed a general framework for efficient parameterized app…

A polynomial bound on the number of minimal separators and potential maximal cliques in P6​-free graphs of bounded clique number

Bounding ε-scatter dimension via metric sparsity

A polynomial bound on the number of minimal separators and potential maximal cliques in $P_{6}$ -free graphs of bounded clique number

Bounding $ε$ -scatter dimension via metric sparsity