# Extending partial representations of circle graphs

@article{Chaplick2013ExtendingPR, title={Extending partial representations of circle graphs}, author={Steven Chaplick and Radoslav Fulek and Pavel Klav{\'i}k}, journal={Journal of Graph Theory}, year={2013}, volume={91}, pages={365 - 394} }

The partial representation extension problem is a recently introduced generalization of the recognition problem. A circle graph is an intersection graph of chords of a circle. We study the partial representation extension problem for circle graphs, where the input consists of a graph G and a partial representation R′ giving some predrawn chords that represent an induced subgraph of G . The question is whether one can extend R ′ to a representation R of the entire graph G , that is, whether one…

## 32 Citations

### Extending Partial Representations of Circle Graphs in Near-Linear Time

- MathematicsMFCS
- 2022

The partial representation extension problem generalizes the recognition problem for geometric intersection graphs. The input consists of a graph G , a subgraph H ⊆ G and a representation H of H .…

### Extending Partial Representations of Circular-Arc Graphs

- Mathematics, Computer ScienceWG
- 2022

It is proved that representation extension problem of unit circular-arc graphs is NP-complete and linear-time algorithms for extending normal proper Helly and proper HellY representations are given.

### Partial and Simultaneous Transitive Orientations via Modular Decomposition

- MathematicsArXiv
- 2022

A natural generalization of the recognition problem for a geometric graph class is the problem of extending a representation of a subgraph to a representation of the whole graph. A related problem is…

### Linear-time Algorithm for Partial Representation Extension of Interval Graphs

- Mathematics, Computer ScienceArXiv
- 2013

A linear-time algorithm based on PQ-trees which solves the problem of recognizing interval graphs by solving whether it is possible to place the remaining interval and create an interval representation R of the entire graph G extending R'.

### Minimal Obstructions for Partial Representations of Interval Graphs

- MathematicsISAAC
- 2014

The minimal obstructions which make partial representations non-extendible of interval graphs are characterized and this characterization leads to a linear-time certifying algorithm for partial representation extension.

### Extending Partial Representations of Proper and Unit Interval Graphs

- Mathematics, Computer ScienceAlgorithmica
- 2016

It is shown that this problem of bounded representations of unit interval graphs, where the input constrains the positions of some intervals by lower and upper bounds, is NP-complete for disconnected input graphs and a linear-time algorithm for extending proper interval representations is given.

### Extension Properties of Graphs and Structures

- Mathematics
- 2017

The main idea of this thesis is to ask what extra information can be deduced from the structure of all possible geometric representations of graphs, namely their automorphism groups, the graph isomorphism problem and regular graph covering.

### Contact Representations of Planar Graphs: Extending a Partial Representation is Hard

- MathematicsWG
- 2014

These are the first classes of geometric graphs where extending partial representations is provably harder than recognition, as opposed to e.g. interval graphs, circle graphs, permutation graphs or even standard representations of plane graphs.

### Extending Partial Representations of Trapezoid Graphs

- MathematicsWG
- 2017

The complexity of partial representation extension for one of the two major remaining classes of geometric intersection graphs for which it has been unknown (circular-arc graphs being the other) is determined.

### Title : Algorithmic aspects of intersection-defined graph classes

- Mathematics
- 2019

Geometrically representable graphs are extensively studied area of research in contemporary literature due to their structural characterizations and efficient algorithms. The most frequently studied…

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A linear-time algorithm based on PQ-trees which solves the problem of recognizing interval graphs by solving whether it is possible to place the remaining interval and create an interval representation R of the entire graph G extending R'.

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The minimal obstructions which make partial representations non-extendible of interval graphs are characterized and this characterization leads to a linear-time certifying algorithm for partial representation extension.

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These are the first classes of geometric graphs where extending partial representations is provably harder than recognition, as opposed to e.g. interval graphs, circle graphs, permutation graphs or even standard representations of plane graphs.

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