English

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 XX-axis, distance 1+ϵ1 + \epsilon (0<ϵ<10 < \epsilon < 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 NP-hard. We present a polynomial time algorithm for recognizing trees that admit a 2SUIG representation.

Keywords

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}
}
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