Maintaining ${\mathsf{CMSO}}_2$ properties on dynamic structures with bounded feedback vertex number

Konrad Majewski, Michał Pilipczuk, Marek Sokołowski

Let $\phi$ be a sentence of ${\mathsf{CMSO}}_2$ (monadic second-order logic with quantification over edge subsets and counting modular predicates) over the signature of graphs. We prese…