On Local Structures of Cubicity 2 Graphs

@inproceedings{Bhore2016OnLS,
  title={On Local Structures of Cubicity 2 Graphs},
  author={Sujoy Kumar Bhore and Dibyayan Chakraborty and Sandip Das and Sagnik Sen},
  booktitle={COCOA},
  year={2016}
}
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 $1 + \epsilon$ ($0 < \epsilon < 1$) 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… 
1 Citations
On Rectangle Intersection Graphs with Stab Number at Most Two
TLDR
It is proved that the Chromatic Number problem is NP-complete even for 2-SRIGs, and it is shown that triangle-free 2- SRIGs are three colorable.

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