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math.CO2026
Merge-width and First-Order Model Checking
Jan Dreier, Szymon ToruÅczyk
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.CO2025
Separability Properties of Monadically Dependent Graph Classes
Ãdouard Bonnet, Samuel Braunfeld, Ioannis Eleftheriadis +5
A graph class is monadically dependent if one cannot interpret all graphs in colored graphs from using a fixed first-order interpretation. We prove that m…