# 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}
}
• S. Bhore, +1 author Sagnik Sen
• Published in COCOA 31 March 2016
• Mathematics, Computer Science
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

## Figures and Topics from this paper

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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.

## References

SHOWING 1-10 OF 15 REFERENCES
On a Special Class of Boxicity 2 Graphs
• Mathematics, Computer Science
CALDAM
• 2015
It turns out that for 2SIG, the chromatic number of any of its induced subgraphs is bounded by twice of its (induced subgraph) clique number, which shows that the graph, even though not perfect, is not very far from it.
Recognizing graphs with fixed interval number is NP-complete
• Computer Science, Mathematics
Discret. Appl. Math.
• 1984
The interval number i(G) of a graph G is the smallest number t such that G has a t-representation, and it is proved that, for any fixed value of t with t≥2, determining whether i( G)≤t is NP-complete is NP -complete.
Approximating the Cubicity of Trees
• Computer Science, Mathematics
ArXiv
• 2014
A randomized algorithm that runs in polynomial time and computes cube representations of trees, of dimension within a constant factor of the optimum, which is the first constant factor approximation algorithm for computing the cubicity of trees.
Unit disk graphs
• Computer Science, Mathematics
Discret. Math.
• 1990
It is shown that many standard graph theoretic problems remain NP-complete on unit disks, including coloring, independent set, domination, independent domination, and connected domination; NP-completeness for the domination problem is shown to hold even for grid graphs, a subclass of unit disk graphs.
Finding the Connected Components and a Maximum Clique of an Intersection Graph of Rectangles in the Plane
• Mathematics, Computer Science
J. Algorithms
• 1983
Algorithms for two problems on intersection graphs of rectangles in the plane for finding the connected components of an intersection graph of n rectangles and an O(n log n) algorithm for finding a maximum clique of such a graph are described.
Algorithmic aspects of constrained unit disk graphs
• Mathematics
• 1996
Computational problems on graphs often arise in two- or three-dimensional geometric contexts. Such problems include assigning channels to radio transmitters (graph colouring), physically routing
Characterizing intersection classes of graphs
The main result is generalized for classes in which the assignment of sets to vertices must be one-to-one, as well as for classes of simplicial complexes arising as nerves of sets from a pre-specified family.
Algorithmic graph theory and perfect graphs
Algorithmic Graph Theory and Perfect Graphs, first published in 1980, has become the classic introduction to the field. This new Annals edition continues to convey the message that intersection graph
Independent and Hitting Sets of Rectangles Intersecting a Diagonal Line: Algorithms and Complexity
• Mathematics, Computer Science
Discret. Comput. Geom.
• 2015
The upper bound follows from simple combinatorial arguments, whereas the lower bound represents the best known lower bound on the duality gap, even in the general setting of the rectangles.
The Complexity of Minimizing Wire Lengths in VLSI Layouts
• Computer Science, Mathematics
Inf. Process. Lett.
• 1987
Abstract Deciding if a graph has a VLSI layout with a specified maximum edge length is NP-complete.