Model Checking Disjoint-Paths Logic on Topological-Minor-Free Graph Classes - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2024

Model Checking Disjoint-Paths Logic on Topological-Minor-Free Graph Classes

Résumé

Disjoint-paths logic, denoted FO+ DP, extends first-order logic (FO) with atomic predicates dpk[(x1, y1), …, (xk, yk)], expressing the existence of internally vertex-disjoint paths between xi and yi, for 1 ≤ i ≤ k. We prove that for every graph class excluding some fixed graph as a topological minor, the model checking problem for FO+ DP is fixed-parameter tractable. This extends the model checking algorithm of Golovach et al. [SODA 2023] for FO+ DP for minor-closed graph classes. It also essentially settles the question of tractable model checking for this logic on subgraph-closed classes, since the problem is hard on subgraph-closed classes not excluding a topological minor (assuming a further mild condition on efficiency of encoding).
Fichier non déposé

Dates et versions

hal-04625781 , version 1 (26-06-2024)

Identifiants

Citer

Nicole Schirrmacher, Sebastian Siebertz, Giannos Stamoulis, Dimitrios Thilikos, Alexandre Vigny. Model Checking Disjoint-Paths Logic on Topological-Minor-Free Graph Classes. LICS 2024 - 39th ACM/IEEE Symposium on Logic in Computer Science, Jul 2024, Tallinn, Estonia. pp.1-12, ⟨10.1145/3661814.3662089⟩. ⟨hal-04625781⟩
24 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More