Grid obstacle representation of graphs
نویسندگان
چکیده
The grid obstacle representation, or alternately, ℓ1-obstacle representation of a graph G=(V,E) is an injective function f:V→Z2 and set point obstacles O on the points Z2 (where no vertex V has been mapped) such that uv edge in G if only there exists Manhattan path between f(u) f(v) avoiding f(V). This work shows planar graphs admit while exist some non-planar do not representation. Moreover, we show every admits Z3. We also NP-hardness result for embeddability
منابع مشابه
Grid obstacle representation of graphs
The grid obstacle representation of a graph G = (V,E) is an injective function f : V → Z and a set of point obstacles O on the grid points of Z (where V has not been mapped) such that uv is an edge in G if and only if there exists a Manhattan path between f(u) and f(v) in Z avoiding the obstacles of O. The grid obstacle number of a graph is the smallest number of obstacles needed for the grid o...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2021
ISSN: ['1872-6771', '0166-218X']
DOI: https://doi.org/10.1016/j.dam.2020.09.027