# circular coloring

## Circular colouring the orthogonality graph ★★

Author(s): DeVos; Ghebleh; Goddyn; Mohar; Naserasr

Let ${\mathcal O}$ denote the graph with vertex set consisting of all lines through the origin in ${\mathbb R}^3$ and two vertices adjacent in ${\mathcal O}$ if they are perpendicular.

\begin{problem} Is $\chi_c({\mathcal O}) = 4$? \end{problem}

Keywords: circular coloring; geometric graph; orthogonality

## Circular coloring triangle-free subcubic planar graphs ★★

\begin{problem} Does every triangle-free planar graph of maximum degree three have circular chromatic number at most $\frac{20}{7}$? \end{problem}

Keywords: circular coloring; planar graph; triangle free