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LexBFS, Structure, and Algorithms

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  • First Online:
Encyclopedia of Algorithms

  • 163 Accesses

Years and Authors of Summarized Original Work

  • 2014; Aboulker, Charbit, Trotignon, Vušković

Problem Definition

We provide a general method to prove the existence and compute efficiently elimination orderings in graphs. Our method relies on several tools that were known before but that were not put together so far: the algorithm LexBFS due to Rose, Tarjan, and Lueker, one of its properties discovered by Berry and Bordat, and a local decomposition property of graphs discovered by Maffray, Trotignon, and Vušković.

Terminology

In this paper, all graphs are finite and simple. A graph G contains a graph F if F is isomorphic to an induced subgraph of G. A class of graphs is hereditary if for every graph G of the class, all induced subgraphs of G belong to the class. A graph G is F-free if it does not contain F. When \(\mathcal{F}\) is a set of graphs, G is \(\mathcal{F}\)-free if it is F-free for every \(F \in \mathcal{F}\). Clearly every hereditary class of graphs is equal to the class of \(\mathcal{F}\)...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Laboratoire de l’Informatique du Parallélisme (LIP), CNRS, ENS de Lyon, Lyon, France

    Nicolas Trotignon

Authors
  1. Nicolas Trotignon
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Correspondence to Nicolas Trotignon .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Trotignon, N. (2016). LexBFS, Structure, and Algorithms. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_687

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