Given a graph $ G $ and a vertex set $ X $, the annotated treewidth tw $(G, X) $ of $ X $ in $
G $ is the maximum treewidth of an $ X $-rooted minor of $ G $, ie, a minor $ H $ where the …

First-order logic (FO) can express many algorithmic problems on graphs, such as the
independent set and dominating set problem parameterized by solution size. However, FO …

The disjoint paths logic, FOL+ DP, is an extension of First-Order Logic (FOL) with the extra
atomic predicate dp k (x 1, y 1,…, xk, yk), expressing the existence of internally vertex …

We introduce a novel model-theoretic framework inspired from graph modification and
based on the interplay between model theory and algorithmic graph minors. The core of our …

Tractability results for the model checking problem of logics yield powerful algorithmic meta
theorems of the form: Every computational problem expressible in a logic $ L $ can be …

A linkage in a graph of size is a subgraph of whose connected components are paths. The
pattern of a linkage of size is the set of pairs formed by the endpoints of these paths. A …

An equivalence class in a set is a subset of elements considered equivalent according to
some criterion. This concept is applied to different graph parameters, such as neighborhood …

First-order logic (FO) can express many algorithmic problems on graphs, such as the
independent set and dominating set problem parameterized by solution size. On the other …

V této dizertační práci se zabýváme rodinou problémů pokrývání podgrafů. Soustředíme se
zejména na problém F-Subgraph Vertex Deletion (F-SVD), kde F je konečná množina …

L'exploration de la tractabilité des problèmes de calcul est un défi majeur de l'informatique
théorique. Une question centrale est de savoir quand, comment et pourquoi les problèmes …