Open Problems from CCCG 2002

2 00 2 Open Problems from CCCG 2002

Is every zonohedron 3-colorable when viewed as a planar map? This question arose out of work described in [RSW01]. An equivalent question, under a different guise, is posed in [FHNS00]: Is the arrangement graph of great circles on the sphere 3colorable? Assume no three circles meet at a point, so that this graph is 4-regular. Circle graphs in the plane can require four colors [Koe90], so the ke...

2 Open Problems from CCCG 2002

Is every zonohedron 3-colorable when viewed as a planar map? This question arose out of work described in [RSW01]. An equivalent question, under a different guise, is posed in [FHNS00]: Is the arrangement graph of great circles on the sphere 3colorable? Assume no three circles meet at a point, so that this graph is 4-regular. Circle graphs in the plane can require four colors [Koe90], so the ke...

1-bend 3-D orthogonal drawings: two open problems solved

Open Problems: Open Problems from CCCG 2005

Consider the following special case of planar point location: preprocess k sets of lines, where each set consists of parallel lines, to support queries of the form “given a point p, what is the line immediately above or below p?” What is the fastest possible query time as a function of k and the total number n of lines? In other words, the n given lines have k distinct orientations. See Figure ...

Open problems from cccg 2001

Refer to Figure 1. A monotone matching is a set of n segments, each the portion of a unique pseudoline, and each spanning a unique slab, such that the left endpoint of each segment is above the right endpoint of the segment in the previous slab. In addition, the point on the first vertical line is below the left endpoint of the first segment, and the point on the last vertical line is above the...