Cograph generation with linear delay

Cograph generation with linear delay

Cographs have always been a research target in areas such as coloring, graph decomposition, and spectral theory. In this work, we present an algorithm to generate all unlabeled cographs with \(n\) vertices, based on the generation of cotrees. The delay of our algorithm (time spent between two consec...

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Veröffentlicht in:arXiv.org 2016-12
Hauptverfasser: Jones, Átila A, Protti, Fábio, Del-Vecchio, Renata R
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Sprache:eng
Schlagworte:
Algorithms
Apexes
Coloring
Computer Science - Discrete Mathematics
Delay
Mathematics - Combinatorics
Spectral theory
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description Cographs have always been a research target in areas such as coloring, graph decomposition, and spectral theory. In this work, we present an algorithm to generate all unlabeled cographs with \(n\) vertices, based on the generation of cotrees. The delay of our algorithm (time spent between two consecutive outputs) is \(O(n)\). The time needed to generate the first output is also \(O(n)\), which gives an overall \(O(n\,M_n)\) time complexity, where \(M_n\) is the number of unlabeled cographs with \(n\) vertices. The algorithm avoids the generation of duplicates (isomorphic outputs) and produces, as a by-product, a linear ordering of unlabeled cographs wih \(n\) vertices.
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subjects Algorithms
Apexes
Coloring
Computer Science - Discrete Mathematics
Delay
Mathematics - Combinatorics
Spectral theory
title Cograph generation with linear delay
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