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math.CO2025
Merge-width and First-Order Model Checking
Jan Dreier, Szymon Toruńczyk
We introduce merge-width, a family of graph parameters that unifies several structural graph measures, including treewidth, degeneracy, twin-width, clique-width, and generalized co…
math.CO2024★ 1 cited
Flip-Breakability: A Combinatorial Dichotomy for Monadically Dependent Graph Classes
Jan Dreier, Nikolas Mählmann, Szymon Toruńczyk
A conjecture in algorithmic model theory predicts that the model-checking problem for first-order logic is fixed-parameter tractable on a hereditary graph class if and only if the…