Your rugby mates don't need to know your colleagues: Triadic closure with edge colors

Laurent Bulteau, Niels Grüttemeier, Christian Komusiewicz, Manuel Sorge

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Given an undirected graph G=(V,E) the NP-hard Strong Triadic Closure (STC) problem asks for a labeling of the edges as weak and strong such that at most k edges are weak and for each induced P3 in G at least one edge is weak. We study the following generalizations of STC with c different strong edge colors. In Multi-STC an induced P3 may receive two strong labels as long as they are different. In Edge-List Multi-STC and Vertex-List Multi-STC we may restrict the set of permitted colors for each edge of G. We show that, under the Exponential Time Hypothesis (ETH), Edge-List Multi-STC and Vertex-List Multi-STC cannot be solved in time 2o(|V|2). We proceed with a parameterized complexity analysis in which we extend previous algorithms and kernelizations for STC [11,14] to the three variants or outline the limits of such an extension.

Original languageEnglish
Pages (from-to)75-96
Number of pages22
JournalJournal of Computer and System Sciences
StatePublished - 1 Sep 2021
Externally publishedYes


  • Edge coloring
  • Exponential time hypothesis
  • Fixed-parameter tractability
  • Kernelization
  • Social network analysis

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics


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