2 citations · 3 across the 6 of their papers we have counts for
8 papers
A Logic for Minor-Free Graph Classes: Model Checking, Dependence, and Combinatorial Reconfiguration
Nikolas Mählmann, Patrice {Ossona de Mendez}, Nicole Schirrmacher +4
We introduce \emph{sub-connectivity logic}, denoted by , an extension of first-order logic for graphs with a specified set of admissible edges. Its additional…
Hereditary 2-WQO Graph Classes Have Bounded Clique-Width
Julien Duron, Nikolas Mählmann, Szymon Toruńczyk
A graph class is -WQO if its -labeled graphs are well-quasi-ordered under label-preserving induced subgraph embeddings. We show that every hereditary graph class that is -…
Fatness and Flatness
Arnold Filtser, Hung Le, Nikolas Mählmann +2
Fat minors are the metric analog of graph minors that are tailored to the analysis of metric (edge-weighted) graphs and, more generally, metric spaces having a suitable notion of s…
Neighborhood Complexity and Radius-1 Merge-Width in Monadically Dependent Graph Classes
Jan Dreier, Nikolas Mählmann, Rose McCarty +2
Monadic dependence is a proposed structural dividing line for fixed-parameter tractability of first-order model checking on hereditary graph classes. A graph class is \emph{monadic…
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…
First-Order Model Checking on Monadically Stable Graph Classes
Jan Dreier, Ioannis Eleftheriadis, Nikolas Mählmann +3
A graph class is called monadically stable if one cannot interpret, in first-order logic, arbitrary large linear orders in colored graphs from . We prove…
First-Order Model Checking on Structurally Sparse Graph Classes
Jan Dreier, Nikolas Mählmann, Sebastian Siebertz
A class of graphs is structurally nowhere dense if it can be constructed from a nowhere dense class by a first-order transduction. Structurally nowhere dense classes vastly general…
Combinatorial and Algorithmic Aspects of Monadic Stability
Jan Dreier, Nikolas Mählmann, Amer E. Mouawad +2
Nowhere dense classes of graphs are classes of sparse graphs with rich structural and algorithmic properties, however, they fail to capture even simple classes of dense graphs. Mon…