14 problems

Let $\Gamma$ be an infinite group. A gain-graphic matroid is the matroid associated with a graph whose edges are labelled by elements of $\Gamma$ according to the gain-graphic cons…

Let $\Gamma$ be a finite group. A gain-graphic matroid is the matroid associated with a graph whose edges are labelled by elements of $\Gamma$ according to the gain-graphic constru…

Linear cliquewidth CMSO obstruction conjecture. A class of graphs $\mathscr{C}$ has bounded linear cliquewidth if and only if the class of trees cannot be $\mathsf{CMSO}$-transduce…

Let $\mathscr{C}$ be a class of graphs, and consider the satisfiability problem for monadic second-order logic ($\mathsf{MSO}$) on $\mathscr{C}$. Seese's bounded-cliquewidth conjec…

Let … the class of all paths, … the class of all graphs. For graph classes … , write $\trianglelefteq_{}$ when there is an MSO transduction from … , and write $\triangleleft_{}$ wh…

Let $H$ be an infinite group. A gain-graphic matroid is a frame matroid obtained from a graph with edge gains in $H$, and a class is characterised by a sentence in monadic second-o…

Let $H$ be a group. A lift matroid is a matroid in Zaslavsky's class of lift matroids, and a quasi-graphic matroid is a matroid in the class of quasi-graphic matroids. The monadic…

A matroid is a finite set system with an independence structure, and a frame matroid is a matroid arising from a biased graph; the monadic second-order language of matroids is the…

Let $H$ be an infinite group, and consider the class of rank-$3$ $H$-gain-graphic matroids. Undecidability conjecture. This class has an undecidable ${\mathit{MS}_{0}}$ theory. The…

Let $H$ be an infinite group. Let ${\mathit{CMS}_{0}}$ denote counting monadic second-order logic over matroids without quantification over edge sets. Non-definability conjecture.…

A lattice path matroid is the matroid represented by a lattice path in the standard lattice-path construction. Let ${\mathit{MS}_{0}}$ denote monadic second-order logic over matroi…

Let $\mathcal{C}$ be a VR-equational class of graphs. Say that $\mathcal{C}$ has property $\mathsf{SEP}$ when it satisfies the separation property defined in the surrounding theory…

Let the paper's main theorem be the assertion referred to as Theorem $\mathrm{main2}$, concerning the limitations of finite axiomatization in $M$-logic. MSOL strengthening conjectu…

Difficult Point Property conjecture. The Difficult Point Property holds for a wide class of graph polynomials, namely graph polynomials definable in Monadic Second Order Logic.