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Unifying Duality Theorems for Width Parameters in Graphs and Matroids (Extended Abstract) Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Colored Modular and Split Decompositions of Graphs with Applications to Trigraphs

Authors : Michel Habib, Antoine Mamcarz

Published in: Graph-Theoretic Concepts in Computer Science

Publisher: Springer International Publishing

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Abstract

We introduce the colored decompositions framework, in which vertices of the graph can be equipped with colors, and in which the goal is to find decompositions of this graph that do not separate the color classes. In this paper, we give two linear time algorithms for the colored modular and split decompositions of graphs, and we apply them to give linear time algorithms for the modular and split decompositions of trigraphs, which improves a result of Thomassé, Trotignon and Vuskovic (2013). As a byproduct, we introduce the non-separating families that allow us to prove that those two decompositions have the same properties on graphs and on trigraphs.

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previous chapter Parameterized Directed -Chinese Postman Problem and Arc-Disjoint Cycles Problem on Euler Digraphs
next chapter Edge Elimination in TSP Instances
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Metadata
Title
Colored Modular and Split Decompositions of Graphs with Applications to Trigraphs
Authors
Michel Habib
Antoine Mamcarz
Copyright Year
2014
Book
Graph-Theoretic Concepts in Computer Science

Print ISBN: 978-3-319-12339-4

Electronic ISBN: 978-3-319-12340-0

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-12340-0_22

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