B1-EPG representations using block-cutpoint trees

@article{Luca2021B1EPGRU,
  title={B1-EPG representations using block-cutpoint trees},
  author={Vitor Tocci F. de Luca and Fabiano S. Oliveira and Jayme Luiz Szwarcfiter},
  journal={ArXiv},
  year={2021},
  volume={abs/2106.05312}
}
In this paper, we are interested in the edge intersection graphs of paths of a grid where each path has at most one bend, called B1-EPG graphs and first introduced by Golumbic et al (2009). We also consider a proper subclass of B1-EPG, the x-EPG graphs, which allows paths only in “x” shape. We show that two superclasses of trees are B1-EPG (one of them being the cactus graphs). On the other hand, we show that the block graphs are x-EPG and provide a linear time algorithm to produce x-EPG… 

References

SHOWING 1-9 OF 9 REFERENCES

On Edge Intersection Graphs of Paths with 2 Bends

On edge-intersection graphs of k-bend paths in grids

It is shown that for any k, if the number of bends in each path is restricted to be at most k , then not all graphs can be represented.

Edge intersection graphs of single bend paths on a grid

This work combines the known notion of the edge intersection graphs of paths in a tree with a VLSI grid layout model and proves that any tree is a B1‐EPG graph and that single bend paths on a grid have Strong Helly number 3.

Edge-intersection graphs of grid paths: The bend-number

Some properties of edge intersection graphs of single bend paths on a grid

  • B. Ries
  • Mathematics
    Electron. Notes Discret. Math.
  • 2009

Testing for the Consecutive Ones Property, Interval Graphs, and Graph Planarity Using PQ-Tree Algorithms

Monotonic Representations of Outerplanar Graphs as Edge Intersection Graphs of Paths on a Grid

It is shown that for any maximal outerplanar graph and any cactus a (monotonic) EPG representation with the smallest possible number of bends can be constructed in a time which is polynomial in the number of vertices of the graph.

On the Bend-Number of Planar and Outerplanar Graphs

The bend-numberb(G) of a graph G is the minimum k such that G may be represented as the edge intersection graph of a set of grid paths with at most k bends. We confirm a conjecture of Biedl and Stern

Stretching a Knock-Knee Layout for Multilayer Wiring

A 4/3 approximation algorithm for the corresponding problem in three layers, shown to be NP-complete, is devised.