Representations of graphs on a cylinder
SIAM Journal on Discrete Mathematics
Rectangle-visibility representations of bipartite graphs
Discrete Applied Mathematics
Characterizing bar line-of-sight graphs
SCG '85 Proceedings of the first annual symposium on Computational geometry
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
On Representations of Some Thickness-Two Graphs
GD '95 Proceedings of the Symposium on Graph Drawing
On Polar Visibility Representations of Graphs
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
On Polar Visibility Representations of Graphs
GD '00 Proceedings of the 8th International Symposium on Graph Drawing
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We characterize two types of bar-visibility 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 block-cutpoint tree of G is a caterpillar in which all but at most one block is planar; and the non-planar block, if it exists, is at the "head" of the caterpillar.