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Reconfiguration of Digraph Homomorphisms

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Titel: Reconfiguration of Digraph Homomorphisms
Autoren: Lévêque, Benjamin, Mühlenthaler, Moritz, Suzan, Thomas
Weitere Verfasser: Benjamin Lévêque and Moritz Mühlenthaler and Thomas Suzan, Optimisation Combinatoire (G-SCOP_OC), Laboratoire des sciences pour la conception, l'optimisation et la production (G-SCOP), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP), Université Grenoble Alpes (UGA)
Quelle: SIAM Journal on Discrete Mathematics. 39:327-360
Publication Status: Preprint
Verlagsinformationen: Society for Industrial & Applied Mathematics (SIAM), 2025.
Publikationsjahr: 2025
Schlagwörter: FOS: Computer and information sciences, Combinatorial Reconfiguration, Discrete Mathematics (cs.DM), [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], Digraph Homomorphisms, 0102 computer and information sciences, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], 01 natural sciences, Computer Science - Data Structures and Algorithms, FOS: Mathematics, Mathematics - Combinatorics, Data Structures and Algorithms (cs.DS), Combinatorics (math.CO), ddc:004, Computer Science - Discrete Mathematics
Beschreibung: 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.
Publikationsart: Article
Conference object
Report
Dateibeschreibung: application/pdf
Sprache: English
ISSN: 1095-7146
0895-4801
DOI: 10.1137/23m1623690
DOI: 10.48550/arxiv.2205.09210
DOI: 10.4230/lipics.stacs.2023.43
Zugangs-URL: http://arxiv.org/abs/2205.09210
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.43
Rights: arXiv Non-Exclusive Distribution
CC BY
Dokumentencode: edsair.doi.dedup.....d2dd2f29b1a9e4c23a416e44f13e08ee
Datenbank: OpenAIRE
Beschreibung
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.
ISSN:10957146
08954801
DOI:10.1137/23m1623690