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On the Capture Time of Cops and Robbers Game on a Planar Graph Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Finding Disjoint Paths on Edge-Colored Graphs: A Multivariate Complexity Analysis

Authors : Riccardo Dondi, Florian Sikora

Published in: Combinatorial Optimization and Applications

Publisher: Springer International Publishing

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Abstract

The problem of finding the maximum number of vertex-disjoint uni-color paths in an edge-colored graph (MaxCDP) has been recently introduced in literature, motivated by applications in social network analysis. In this paper we investigate how the complexity of the problem depends on graph parameters (distance from disjoint paths and size of vertex cover), and that is not FPT-approximable. Moreover, we introduce a new variant of the problem, called MaxCDDP, whose goal is to find the maximum number of vertex-disjoint and color-disjoint uni-color paths. We extend some of the results of MaxCDP to this new variant, and we prove that unlike MaxCDP, MaxCDDP is already hard on graphs at distance two from disjoint paths.

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previous chapter Improved Precise Fault Diagnosis Algorithm for Hypercube-Like Graphs
next chapter Total Dual Integrality of Triangle Covering
Footnotes
1
A graph is cubic when each of its vertices has degree 3.
 
2
Notice that, since \(|X| \leqslant d\), X can be computed in time \(O(n^d)\).
 
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Metadata
Title
Finding Disjoint Paths on Edge-Colored Graphs: A Multivariate Complexity Analysis
Authors
Riccardo Dondi
Florian Sikora
Copyright Year
2016
Book
Combinatorial Optimization and Applications

Print ISBN: 978-3-319-48748-9

Electronic ISBN: 978-3-319-48749-6

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-48749-6_9

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