6 problems

Huynh's characterization conjecture. For minor-closed classes of graphs, the bounded-dimension property holds exactly for those classes that exclude the cover graph of a poset in K…

Let $H$ be a fixed graph, and let a poset's cover graph be $H$-minor-free if it contains no $H$ minor. A chain in a poset is a set of pairwise comparable elements; two chains are i…

Let $H$ be a graph. Call $H$ unavoidable if the cover graph of every poset of sufficiently large dimension contains $H$ as a minor. Kelly's construction refers to the family of pla…

Let $P$ be a poset, let $G$ be the cover graph of $P$, and let $Q$ be the incidence poset of $G$. Cover-graph incidence-poset doubling conjecture. For every $t\ge1$, there exists a…

Let $P$ be a poset, let $G$ be its cover graph, let $girth(G)$ denote the length of its shortest cycle, and let $chi(G)$ denote its chromatic number. Bounded-dimension high-girth c…

Let $P$ be a poset, and let its cover graph be the graph whose vertices are the elements of $P$ and whose edges join pairs in a cover relation. A graph is planar if it can be drawn…