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arXiv · 1603.09570

On local structures of cubicity 2 graphs

Sujoy Kumar Bhore·Dibyayan Chakraborty·Sandip Das·Sagnik Sen
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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 $X$-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 known to be NP-hard. We present a polynomial time algorithm for recognizing trees that admit a 2SUIG representation.

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Sujoy Kumar Bhore, Dibyayan Chakraborty, Sandip Das, Sagnik Sen. 2016-03-31. On local structures of cubicity 2 graphs. https://arxiv.org/abs/1603.09570

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