# Edge intersection graphs of single bend paths on a grid

@article{Golumbic2009EdgeIG, title={Edge intersection graphs of single bend paths on a grid}, author={Martin Charles Golumbic and Marina Lipshteyn and Michal Stern}, journal={Networks}, year={2009}, volume={54} }

We combine the known notion of the edge intersection graphs of paths in a tree with a VLSI grid layout model to introduce the edge intersection graphs of paths on a grid. Let 𝒫 be a collection of nontrivial simple paths on a grid 𝒢. We define the edge intersection graph EPG(𝒫) of 𝒫 to have vertices which correspond to the members of 𝒫, such that two vertices are adjacent in EPG(𝒫) if the corresponding paths in 𝒫 share an edge in 𝒢. An undirected graph G is called an edge intersection…

## 47 Citations

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

- MathematicsDiscret. Math. Theor. Comput. Sci.
- 2009

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 grid paths: The bend-number

- MathematicsDiscret. Appl. Math.
- 2014

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

- MathematicsElectron. Notes Discret. Math.
- 2009

Edge Intersection Graphs of Paths on a Triangular Grid

- MathematicsAnais do VII Encontro de Teoria da Computação (ETC 2022)
- 2022

We introduce a new class of intersection graphs, the edge intersection graphs of paths on a triangular grid, called EPGt graphs. We compare this new class with the well-known class of EPG graphs. A…

Graphs of edge-intersecting non-splitting paths in a tree: Representations of holes - Part I

- Mathematics, Computer ScienceDiscret. Appl. Math.
- 2016

The goal is to characterize the representation of chordless ENPT cycles (holes) by providing a polynomial-time algorithm to solve P3-HamiltonianPairRec, unless P=NP.

On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid

- MathematicsElectron. Notes Discret. Math.
- 2015

On $k$-Bend and Monotonic $\ell$-Bend Edge Intersection Graphs of Paths on a Grid

- Mathematics
- 2020

It is proved that B m k $ Bk holds also for k ∈ {2, 3, 5} and for k > 7 and it is shown that restricting the shape of the paths can lead to a significant change in the structure of the graph.

Edge intersection graphs of systems of paths on a grid with a bounded number of bends

- MathematicsDiscret. Appl. Math.
- 2009

Relationship of k-Bend and Monotonic 𝓁-Bend Edge Intersection Graphs of Paths on a Grid

- MathematicsArXiv
- 2020

It is proved that $B_1 \subseteq B_3^m$ holds, providing the first result of this kind and implying that restricting the shape of the paths can lead to a significant increase of the number of bends needed in an EPG representation.

## References

SHOWING 1-10 OF 185 REFERENCES

On Eulerian and Hamiltonian Graphs and Line Graphs

- MathematicsCanadian Mathematical Bulletin
- 1965

A graph G has a finite set V of points and a set X of lines each of which joins two distinct points (called its end-points), and no two lines join the same pair of points. A graph with one point and…

On maximal independent sets of vertices in claw-free graphs

- MathematicsJ. Comb. Theory, Ser. B
- 1980

Intersection Cuts - A New Type of Cutting Planes for Integer Programming

- MathematicsOper. Res.
- 1971

The paper gives a simple formula for finding the equation of the hyperplane, discusses some ways of strengthening the cut, proposes an algorithm, and gives a finiteness proof.

The steiner problem in graphs

- Computer ScienceNetworks
- 1971

An algorithm for solving the Steiner problem on a finite undirected graph is presented. This algorithm computes the set of graph arcs of minimum total length needed to connect a specified set of k…