On local structures of cubicity 2 graphs
Discrete Mathematics
2016-04-01 v1 Combinatorics
Abstract
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 -axis, distance () 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 NP-hard. We present a polynomial time algorithm for recognizing trees that admit a 2SUIG representation.
Cite
@article{arxiv.1603.09570,
title = {On local structures of cubicity 2 graphs},
author = {Sujoy Kumar Bhore and Dibyayan Chakraborty and Sandip Das and Sagnik Sen},
journal= {arXiv preprint arXiv:1603.09570},
year = {2016}
}