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The Parameterized Landscape of Labeled Graph Contractions

Authors Manuel Lafond , Bertrand Marchand

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  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Parameterized complexity - contractions - labels - widths

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Abstract

In this work, we study the problem of computing a maximum common contraction of two vertex-labeled graphs, i.e. how to make them identical by contracting as little edges as possible in the two graphs. We study the problem from a parameterized complexity point of view, using parameters such as the maximum degree, the degeneracy, the clique-width or treewidth of the input graphs as well as the number of allowed contractions. We put this complexity in perspective with that of the labeled contractibility problem, i.e determining whether a labeled graph is a contraction of another. Surprisingly, our results indicate very little difference between these problems in terms of parameterized complexity status. We only prove their status to differ when parameterizing by both the degeneracy and the number of allowed contractions, showing W[1]-hardness of the maximum common contraction problem in this case, whereas the contractibility problem is FPT.

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Manuel Lafond and Bertrand Marchand. The Parameterized Landscape of Labeled Graph Contractions. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 42:1-42:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.WADS.2025.42

Author Details

Manuel Lafond
  • Department of Computer Science, University of Sherbrooke, Canada
Bertrand Marchand
  • Department of Computer Science, University of Sherbrooke, Canada

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