Reconfiguration of Digraph Homomorphisms

Authors Benjamin Lévêque, Moritz Mühlenthaler , Thomas Suzan

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Author Details

Benjamin Lévêque
  • Laboratoire G-SCOP, Grenoble INP, Université Grenoble-Alpes, France
Moritz Mühlenthaler
  • Laboratoire G-SCOP, Grenoble INP, Université Grenoble-Alpes, France
Thomas Suzan
  • Laboratoire G-SCOP, Grenoble INP, Université Grenoble-Alpes, France

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Benjamin Lévêque, Moritz Mühlenthaler, and Thomas Suzan. Reconfiguration of Digraph Homomorphisms. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 43:1-43:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


For a fixed graph H, the H-Recoloring problem asks whether, given two homomorphisms from a graph G to H, one homomorphism can be transformed into the other by changing the image of a single vertex in each step and maintaining a homomorphism to H throughout. The most general algorithmic result for H-Recoloring so far has been proposed by Wrochna in 2014, who introduced a topological approach to obtain a polynomial-time algorithm for any undirected loopless square-free graph H. We show that the topological approach can be used to recover essentially all previous algorithmic results for H-Recoloring and that it is applicable also in the more general setting of digraph homomorphisms. In particular, we show that H-Recoloring admits a polynomial-time algorithm i) if H is a loopless digraph that does not contain a 4-cycle of algebraic girth 0 and ii) if H is a reflexive digraph that contains no triangle of algebraic girth 1 and no 4-cycle of algebraic girth 0.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Discrete mathematics
  • Digraph Homomorphisms
  • Combinatorial Reconfiguration


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