5 problems

A tournament $R$ is a rebel if the class of tournaments not containing $R$ has bounded domination number. A poset tournament is a tournament admitting an ordering whose backedge gr…

Let $G$ be a comparability graph, meaning the graph of a partial order. Write $\mathcal{R}_2$ for the class of graphs with representation number at most two, and…

Let $H$ be a graph. A numbering of a tournament $T$ is an ordering of its vertices, and its backedge graph has an edge for each tournament edge directed backwards in that ordering.…

Near-linear clique conjecture. Then

A poset is a set equipped with a partial order, and a chain is a subset whose elements are pairwise comparable. For a graph $G$, let $\theta(G)$ be the least cardinality of a cover…