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

Giannos Stamoulis
LIRMM, Université de Montpellier, CNRS
March 29, 2023, 2:15 p.m.
room 5050
Seminar Automata Theory

Disjoint-paths logic, denoted FO+DP, extends first-order logic (FO) with atomic predicates dp_k[(x_1, y_1),…,(x_k, y_k)], expressing the existence of internally vertex-disjoint paths between x_i and y_i, for 1 ≤ i ≤ k. In this talk, we first show how to prove (fixed-parameter) tractability of the model checking problem for FO+DP on graph classes excluding some fixed graph as a minor. Then, we sketch how to extend this tractability result to graph classes excluding some fixed graph as a *topological* minor. The latter settles the question of tractable model checking for this logic on subgraph-closed graph classes. Joint work with Petr A. Golovach and Dimitrios M. Thilikos and Nicole Schirrmacher, Sebastian Siebertz, Dimitrios M. Thilikos, and Alexandre Vigny.