Twin-Width Is Linear in the Poset Width

Authors Jakub Balabán, Petr Hliněný

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Author Details

Jakub Balabán
  • Masaryk University, Brno, Czech Republic
Petr Hliněný
  • Masaryk University, Brno, Czech Republic

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Jakub Balabán and Petr Hliněný. Twin-Width Is Linear in the Poset Width. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Twin-width is a new parameter informally measuring how diverse are the neighbourhoods of the graph vertices, and it extends also to other binary relational structures, e.g. to digraphs and posets. It was introduced just very recently, in 2020 by Bonnet, Kim, Thomassé and Watrigant. One of the core results of these authors is that FO model checking on graph classes of bounded twin-width is in FPT. With that result, they also claimed that posets of bounded width have bounded twin-width, thus capturing prior result on FO model checking of posets of bounded width in FPT. However, their translation from poset width to twin-width was indirect and giving only a very loose double-exponential bound. We prove that posets of width d have twin-width at most 8d with a direct and elementary argument, and show that this bound is tight up to a constant factor. Specifically, for posets of width 2 we prove that in the worst case their twin-width is also equal 2. These two theoretical results are complemented with straightforward algorithms to construct the respective contraction sequence for a given poset.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorics
  • Mathematics of computing → Graph algorithms
  • twin-width
  • digraph
  • poset
  • FO model checking
  • contraction sequence


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