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Maximum Edge-Colorable Subgraph and Strong Triadic Closure Parameterized by Distance to Low-Degree Graphs

Authors Niels Grüttemeier , Christian Komusiewicz , Nils Morawietz

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Niels Grüttemeier
  • Philipps-Universität Marburg, Fachbereich Mathematik und Informatik, Germany
Christian Komusiewicz
  • Philipps-Universität Marburg, Fachbereich Mathematik und Informatik, Germany
Nils Morawietz
  • Philipps-Universität Marburg, Fachbereich Mathematik und Informatik, Germany

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Niels Grüttemeier, Christian Komusiewicz, and Nils Morawietz. Maximum Edge-Colorable Subgraph and Strong Triadic Closure Parameterized by Distance to Low-Degree Graphs. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.SWAT.2020.26

Abstract

Given an undirected graph G and integers c and k, the Maximum Edge-Colorable Subgraph problem asks whether we can delete at most k edges in G to obtain a graph that has a proper edge coloring with at most c colors. We show that Maximum Edge-Colorable Subgraph admits, for every fixed c, a linear-size problem kernel when parameterized by the edge deletion distance of G to a graph with maximum degree c-1. This parameterization measures the distance to instances that, due to Vizing’s famous theorem, are trivial yes-instances. For c≤ 4, we also provide a linear-size kernel for the same parameterization for Multi Strong Triadic Closure, a related edge coloring problem with applications in social network analysis. We provide further results for Maximum Edge-Colorable Subgraph parameterized by the vertex deletion distance to graphs where every component has order at most c and for the list-colored versions of both problems.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Fixed parameter tractability
Keywords
  • Graph coloring
  • social networks
  • parameterized complexity
  • kernelization

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References

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