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Pré-Publication, Document De Travail Année : 2022

Reconfiguration of Digraph Homomorphisms

Résumé

For a fixed graph H, the H-Recoloring problem asks whether for two given homomorphisms from a graph G to H, we can transform one into the other by changing the image of a single vertex of G in each step and maintaining a homomorphism from G to H throughout. We extend an algorithm of Wrochna for H-Recoloring where H is a square-free loopless undirected graph to the more general setting of directed graphs. We obtain a polynomial-time algorithm for H-Recoloring in this setting whenever H is a loopless digraph that does not contain a 4-cycle of algebraic girth zero and whenever H is a reflexive digraph that contains neither a 3-cycle of algebraic girth 1 nor a 4-cycle of algebraic girth zero.
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Dates et versions

hal-04215572 , version 1 (22-09-2023)

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Benjamin Lévêque, Moritz Mühlenthaler, Thomas Suzan. Reconfiguration of Digraph Homomorphisms. 2023. ⟨hal-04215572⟩
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