# Giannos Stamoulis, Model-Checking for First-Order Logic with Disjoint Paths Predicates in Proper Minor-Closed Graph Classes

## November 29 Tuesday @ 4:30 PM - 5:30 PM KST

Room B332, IBS (기초과학연구원)

### Speaker

Giannos Stamoulis
LIRMM, Université de Montpellier, CNRS, Montpellier, France
https://www.lirmm.fr/~gstamoulis/

The disjoint paths logic, FOL+DP,  is an extension of First Order Logic (FOL) with the extra atomic predicate $\mathsf{dp}_k(x_1,y_1,\ldots,x_k,y_k),$ expressing the existence of internally vertex-disjoint paths between $x_i$ and $y_i,$ for $i\in \{1,\ldots, k\}$. This logic can express a wide variety of problems that escape the expressibility potential of FOL. We prove that for every minor-closed graph class, model-checking for FOL+DP can be done in quadratic time. We also introduce an extension of FOL+DP, namely the scattered disjoint paths logic, FOL+SDP, where we further consider the atomic predicate $\mathsf{s-sdp}_k(x_1,y_1,\ldots,x_k,y_k),$ demanding that the disjoint paths are within distance bigger than some fixed value $s$. Using the same technique we prove that model-checking for FOL+SDP can be done in quadratic time on classes of graphs with bounded Euler genus.
Joint work with Petr A. Golovach and Dimitrios M. Thilikos.

## Details

Date:
November 29 Tuesday
Time:
4:30 PM - 5:30 PM KST
Event Category:
Event Tags:

Room B332
IBS (기초과학연구원)