On local structures of cubicity 2 graphs [article]

Sujoy Kumar Bhore, Dibyayan Chakraborty, Sandip Das, Sagnik Sen
2016 arXiv   pre-print
A 2-stab unit interval graph (2SUIG) is an axes-parallel unit square intersection graph where the unit squares intersect either of the two fixed lines parallel to the X-axis, distance 1 + ϵ (0 < ϵ < 1) apart. This family of graphs allow us to study local structures of unit square intersection graphs, that is, graphs with cubicity 2. The complexity of determining whether a tree has cubicity 2 is unknown while the graph recognition problem for unit square intersection graph is known to be
more » ... We present a polynomial time algorithm for recognizing trees that admit a 2SUIG representation.
arXiv:1603.09570v1 fatcat:pohuogwanzeqfp4ibparjjhqmi