7 problems

Let a separating cut be a cut in a matchable graph whose contraction produces a graph, and let $\operatorname{pf}(G)$ denote the pfaffian number of a graph $G$. Separating-cut pres…

Isomorphism conjecture. The map $\Phi$ is an isomorphism, hence $\mathbf U_I$ is a split subquotient of $\mathbf U_{\widehat I}$. This makes the conjectural subquotient statement p…

Subquotient conjecture. The explicit embedding for quantum groups in Theorem is a section of a subquotient. This conjecture is motivated by the corresponding result for Hall algebr…

Let $G$ be a graph and let $e$ be an edge of $G$. Write $G/e$ for the graph obtained by contracting $e$, and let $\chi_{dom}(G)$ denote the dominated chromatic number of $G$. Edge-…

Let $D=(V,A)$ be a 3-edge-connected digraph. An even subgraph $E\subseteq A$ is an edge-disjoint union of cycles of $D$, where the cycles need not be directed, and $D/E$ is the gra…

Let $G$ be a 3-edge-connected graph of order $n$, and let $\overline{\sigma}_2(G)$ denote the minimum relevant degree-sum parameter. Let $\mathcal{SL}$ denote the class represented…

Let $G$ be a 3-edge-connected simple graph of order at most $17$, let $\mathcal{SL}$ denote the class represented by \text{cal S!L}, and let $P$, $P_{14}$, and $P_{16}$ be the…