5 problems

A class of graphs is self-intersection-closed if it is closed under the self-intersection operation considered in the paper, and a class is finitely-defined when it is specified by…

Characterisation conjecture. The hereditary graph class $\mathcal{G}^\delta$ is minimal of unbounded clique-width if and only if $\delta \in \Delta_{min}$.

Let $\mathcal{F}$ be a hereditary family of graphs such that the number of its $n$-vertex graphs is at most $2^{O(n\log n)}$. An adjacency labelling scheme assigns labels of length…

Lozin–Razgon–Zamaraev's labelled induced-subgraph conjecture. If $\mathcal{G}$ is defined by a finite set of forbidden induced subgraphs, then $\mathcal{G}$ is well-quasi-ordered b…

Lozin–Razgon–Zamaraev's conjecture. If a finitely defined hereditary graph class $\mathcal{G}$ is well-quasi-ordered by the induced subgraph relation, then $\mathcal{G}$ has bounde…