6 problems

For a positive integer $s$, a graph is $K_{s,s}$-free if it contains no subgraph isomorphic to $K_{s,s}$. Linear pivot-minor degree-boundedness conjecture. For each bipartite graph…

A graph class is proper vertex-minor-closed if it is closed under vertex-minors and is not the class of all graphs. It is linearly degree-bounded if there is a linear bound, in the…

Restricted antidirected subdivision conjecture. Every oriented graph $D$ with

A graph class $\mathcal{F}$ is proper if some graph is not isomorphic to any graph in $\mathcal{F}$. Write $int(\mathcal{F})$ for the class of intersection graphs of collections of…

For a graph $G$, let $\tau(G)$ be its biclique number, and call a graph a vertex-minor of $G$ if it can be obtained by taking induced subgraphs and performing local complementation…

For a graph $H$, let $\mathcal{F}_H$ be the class of graphs with no induced subdivision of $H$. A class is polynomially degree-bounded if there is a polynomial $p$ such that every…