7 problems

Chordal graph representation conjecture. Let $H$ be a chordal graph. There are chordal graphs $G$ and $G'$ such that $H$ is isomorphic to both $C(G)$ and $C_R(G')$.

A stable representation is an ${\mathcal{M}}$-representation that is a local minimum with respect to the ordering relation defining stability. Consider a graph on the sphere and fi…

A stable representation of a graph is an ${\mathcal{M}}$-representation that is a local minimum with respect to the ordering relation defining stability. Finite algorithm conjectur…

A graph is representable as a visibility graph if it admits a visibility representation by regions whose unblocked sightlines correspond exactly to the edges of the graph. Connecte…

Let $G$ be a planar graph. For each internal face $F$ in a plane drawing of $G$, let $G_F$ denote the subgraph induced by the vertices incident with $F$. Compact visibility conject…

Let $\mathrm{pdd}(n)$ denote the minimum dimension required to realize a dichotomous ordinal complete graph on $n$ vertices, and let $\mathrm{sp}(G)$ be the sphericity of a graph…

An EPG representation of a graph represents each vertex by a path in the square grid, with adjacency corresponding to sharing a grid edge; a path has a bend at each change of grid…