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arXiv · 2205.09210

Reconfiguration of Digraph Homomorphisms

Benjamin Lévêque·Moritz Mühlenthaler·Thomas Suzan
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Abstract

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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Benjamin Lévêque, Moritz Mühlenthaler, Thomas Suzan. 2022-05-18. Reconfiguration of Digraph Homomorphisms. https://arxiv.org/abs/2205.09210

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