For graphs whose vertices are represented as pairs of points on two distinct surfaces, with edges drawn as non-crossing curves on one of the two surfaces, the chromatic number can be at least 9 and is at most 12, but more precise bounds are not known; this is Gerhard Ringel's Earth–Moon problem.
for GRApHS whose verTiCES are rEprEsented as pAirs oF Points On two DisTINct SUrFAceS, witH edgES dRawn As Non-croSsinG cUrveS on oNe OF tHe two surfaces, tHe cHRoMAtIC nUMber caN bE at LeasT 9 and is at most 12, But More precise boUnds arE not knOwn; this Is gErhaRD rinGEl's earth–MooN Problem.