A Layout Algorithm for BarVisibility Graphs on the Möbius BandDean, Alice M. (2001) A Layout Algorithm for BarVisibility Graphs on the Möbius Band. In: Graph Drawing 8th International Symposium, GD 2000, September 20–23, 2000 , pp. 350359(Official URL: http://dx.doi.org/10.1007/3540445412_33). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/3540445412_33
AbstractWe characterize two types of barvisibility graphs on the Möbius band (abbreviated "BVGMs"), in which vertices correspond to intervals that are parallel or orthogonal to the axis of the band, depending on type, and in which adjacency corresponds to orthogonal visibility of intervals. BVGMs with intervals orthogonal to the axis are shown to be equivalent to the "polar visibility graphs" studied by Hutchinson [7]. BVGMs with intervals parallel to the axis are characterized as those graphs G which satisfy the following conditions: G is embedded on the Möbius band; the blockcutpoint tree of G is a caterpillar in which all but at most one block is planar; and the nonplanar block, if it exists, is at the "head" of the caterpillar.
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