Grid obstacle representation of graphs

Authors

Arijit Bishnu, Indian Statistical Institute, Kolkata
Arijit Ghosh, Indian Statistical Institute, Kolkata
Rogers Mathew, Indian Institute of Technology Hyderabad
Gopinath Mishra, Indian Statistical Institute, Kolkata
Subhabrata Paul, Indian Institute of Technology Patna

Article Type

Research Article

Publication Title

Discrete Applied Mathematics

Abstract

The grid obstacle representation, or alternately, ℓ1-obstacle representation of a graph G=(V,E) is an injective function f:V→Z2 and a set of point obstacles O on the grid points of Z2 (where no vertex of V has 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 Z2 avoiding the obstacles of O and points in f(V). This work shows that planar graphs admit such a representation while there exist some non-planar graphs that do not admit such a representation. Moreover, we show that every graph admits a grid obstacle representation in Z3. We also show NP-hardness result for the point set embeddability of an ℓ1-obstacle representation.

First Page

39

Last Page

51

DOI

10.1016/j.dam.2020.09.027

Publication Date

6-15-2021

Comments

Open Access, Green

Recommended Citation

Bishnu, Arijit; Ghosh, Arijit; Mathew, Rogers; Mishra, Gopinath; and Paul, Subhabrata, "Grid obstacle representation of graphs" (2021). Journal Articles. 1913.
https://digitalcommons.isical.ac.in/journal-articles/1913