# Approximation Algorithms for Intersection Graphs

@article{Kammer2012ApproximationAF, title={Approximation Algorithms for Intersection Graphs}, author={Frank Kammer and Torsten Tholey and Heiko Voepel}, journal={Algorithmica}, year={2012}, volume={68}, pages={312-336} }

We study three complexity parameters that, for each vertex v, are an upper bound for the number of cliques that are sufficient to cover a subset S(v) of its neighbors. We call a graph k-perfectly groupable if S(v) consists of all neighbors, k-simplicial if S(v) consists of the neighbors with a higher number after assigning distinct numbers to all vertices, and k-perfectly orientable if S(v) consists of the endpoints of all outgoing edges from v for an orientation of all edges. These parameters…

## 26 Citations

### Approximation and Online Algorithms

- Mathematics, Computer ScienceLecture Notes in Computer Science
- 2015

This work considers the problem of finding d-regular spanning subgraphs of minimum weight with connectivity requirements and presents approximation algorithms that achieve constant approximation ratios for all d ≥ 2 · k/2 .

### Avoidable Vertices and Edges in Graphs

- MathematicsWADS
- 2019

A polynomial-time algorithm for the maximum weight clique problem in a class of graphs generalizing the class of 1-perfectly orientable graphs and its subclasses chordal graphs and circular-arc graphs is derived using Lexicographic Breadth First Search and bisimplicial elimination orderings.

### Algorithms for Dominating Set in Disk Graphs: Breaking the logn Barrier - (Extended Abstract)

- Mathematics, Computer ScienceESA
- 2010

A randomized algorithm is given that obtains a dominating set whose weight is within a factor 2O(log* n) of a minimum cost solution, with high probability - the technique follows the framework proposed recently by Varadarajan.

### Algorithms for Intersection Graphs of 𝑡 -Intervals and 𝑡 -Pseudodisks

- Mathematics, Computer Science
- 2022

The results are obtained via simple reductions to existing algorithms by appropriately bounding the union complexity of the objects under consideration, and it is shown that it is NP -hard to obtain a polynomial-time approximation ratio for dominating set in the intersection graph of 𝑡 -pseudodisks.

### Algorithms and Bounds for Very Strong Rainbow Coloring

- MathematicsLATIN
- 2018

It is natural to prove that a coloring exists where, for every shortest path between every pair of vertices in the graph, all edges of the path receive different colors.

### Co-Bipartite Neighborhood Edge Elimination Orderings

- Mathematics, Computer ScienceElectron. Notes Discret. Math.
- 2017

### Algorithms for Intersection Graphs of Multiple Intervals and Pseudo Disks

- Mathematics, Computer ScienceArXiv
- 2019

For the minimum weight dominating set problem, a simple $O(t \log t)$ approximation is given for Multiple-Interval Graphs, improving on the previously known bound of $t^2$ and it is shown that it is NP-hard to obtain an $o(t)$-approximation in this case.

### On the structure of 1-perfectly orientable graphs

- MathematicsArXiv
- 2014

We study the class of 1-perfectly orientable (1-p.o.) graphs, that is, graphs having an orientation in which every out-neighborhood induces a tournament. 1-p.o. graphs form a common generalization of…

### An Approach to Hadwiger's Conjecture through Squares of Chordal Graphs

- MathematicsArXiv
- 2016

This work studies a simple subclass of chordal graphs, namely 2-trees and proves Hadwiger’s Conjecture for the square of the same, and shows the following stronger result: If G is thesquare of a 2-tree, then G has a clique minor of size χ(G), where each branch set is a path.

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