# 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}
}
• Published 1 October 2009
• Computer Science
• Networks
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…
On edge-intersection graphs of k-bend paths in grids
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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.
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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
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ICTCS
• 2014
On $k$-Bend and Monotonic $\ell$-Bend Edge Intersection Graphs of Paths on a Grid
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• 2020
It is proved that B m k $Bk holds also for k ∈ {2, 3, 5} and for k > 7 and it is shown that restricting the shape of the paths can lead to a significant change in the structure of the graph. Relationship of k-Bend and Monotonic 𝓁-Bend Edge Intersection Graphs of Paths on a Grid • Mathematics ArXiv • 2020 It is proved that$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.

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