Reconfiguring spanning and induced subgraphs

Hanaka, Tesshu; Ito, Takehiro; Mizuta, Haruka; Moore, Benjamin; Nishimura, Nobuya; Subramanya, Vijay; Suzuki, Ai; Vaidyanathan, Krishna

doi:10.1016/j.tcs.2019.09.018

Cited by 8 publications

(1 citation statement)

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“…Often however the graph H is not fixed, but any subgraph of a certain "shape", e.g., any tree, would be acceptable. We refer the readers to the survey of Nishimura [14] for an overview of known results in this direction, in particular those on the reconfiguration of independent sets, as well as [11] for results on spanning and induced subgraphs. A general introduction to reconfiguration problems that also discusses their relation to combinatorial games and puzzles can be found in [15].…”

Section: Related Workmentioning

confidence: 99%

Reconfiguration of Digraph Homomorphisms

Lévêque¹,

Mühlenthaler²,

Suzan³

2022

Preprint

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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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Section: Related Workmentioning

confidence: 99%