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math.CO2026
Linear clique-width and modular decomposition
Robert Brignall, Michal Opler, Vincent Vatter
A hereditary class of graphs has bounded clique-width if and only if its prime members do, but this lifting property fails for linear clique-width. We prove that a hereditary class…
cs.DS2026
Fast and simple multiplication of bounded twin-width matrices
László Kozma, Michal Opler
Matrix multiplication is a fundamental task in almost all computational fields, including machine learning and optimization, computer graphics, signal processing, and graph algorit…
cs.DS2026
Inapproximability of Counting Permutation Patterns
Michal Opler
Detecting and counting copies of permutation patterns are fundamental algorithmic problems, with applications in the analysis of rankings, nonparametric statistics, and property te…