arrangement graph


3-Colourability of Arrangements of Great Circles ★★

Author(s): Felsner; Hurtado; Noy; Streinu

Consider a set $S$ of great circles on a sphere with no three circles meeting at a point. The arrangement graph of $S$ has a vertex for each intersection point, and an edge for each arc directly connecting two intersection points. So this arrangement graph is 4-regular and planar.

\begin{conjecture} Every arrangement graph of a set of great circles is $3$-colourable. \end{conjecture}

Keywords: arrangement graph; graph coloring

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