Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  characterize two types of bar-visibility graphs on the Mobius 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 Mobius 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.
['Alice M. Dean']
I am writing a research paper on a idea A Layout Algorithm for Bar-Visibility Graphs on the Möbius Band
[{"from": "human", "value": "I am writing a research paper on a idea A Layout Algorithm for Bar-Visibility Graphs on the M\u00f6bius Band"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  characterize two types of bar-visibility graphs on the Mobius 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 Mobius 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."}]