# Gap-Planar Graphs

@inproceedings{Bae2017GapPlanarG, title={Gap-Planar Graphs}, author={Sang Won Bae and Jean-François Baffier and Jinhee Chun and Peter Eades and Kord Eickmeyer and Luca Grilli and Seok-Hee Hong and Matias Korman and Fabrizio Montecchiani and Ignaz Rutter and Csaba D. T{\'o}th}, booktitle={Graph Drawing}, year={2017} }

We introduce the family of k-gap-planar graphs for \(k \ge 0\), i.e., graphs that have a drawing in which each crossing is assigned to one of the two involved edges and each edge is assigned at most k of its crossings. This definition finds motivation in edge casing, as a \(k\)-gap-planar graph can be drawn crossing-free after introducing at most k local gaps per edge. We obtain results on the maximum density, drawability of complete graphs, complexity of the recognition problem, and…

## 16 Citations

On Optimal Beyond-Planar Graphs

- Mathematics
- 2022

The range for optimal graphs is computed, combinatorial properties are established, and it is shown that every graph is a topological minor of an optimal graph.

Crossing Numbers of Beyond-Planar Graphs Revisited

- MathematicsArXiv
- 2021

This paper extends the results of Chimani et al. to the main currently known classes of beyond-planar graphs characterized by forbidden edge configurations and answers several of their open questions.

Efficient Generation of Different Topological Representations of Graphs Beyond-Planarity

- MathematicsGraph Drawing
- 2019

Overcoming the limitations of standard combinatorial arguments, this work presents a technique to systematically generate all non-isomorphic topological representations of complete and complete bipartite graphs, taking into account the constraints of the specific class.

Fan-Crossing Free Graphs

- MathematicsArXiv
- 2020

The fan22 crossing free graphs are shown to be universal for 2-subdivision and for node-to-circle 3 expansion, and universality for an operation and a graph class is introduced, so the every graph has an image in the graph class.

Shallow Minors, Graph Products and Beyond Planar Graphs

- Mathematics
- 2021

The planar graph product structure theorem of Dujmović, Joret, Micek, Morin, Ueckerdt, and Wood [J. ACM 2020] states that every planar graph is a subgraph of the strong product of a graph with…

Beyond Planar Graphs: Communications of NII Shonan Meetings

- MathematicsBeyond Planar Graphs
- 2020

This chapter introduces various types of beyond planar graphs and briefly review known results on the edge density, computational complexity, and algorithms for testing beyondPlanar graphs.

On RAC Drawings of Graphs with one Bend per Edge

- MathematicsGraph Drawing
- 2018

It is shown that an n-vertex 1-bend RAC graph cannot have more than $5.5n-O(1)$ edges, and it is demonstrated that there exist infinitely many n- Vertex1-bends RAC graphs with exactly $5 n-O (1) edges.

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