Reconfiguring spanning and induced subgraphs

Hanaka, Tesshu; Ito, Teruaki; Mizuta, Haruka; Moore, Benjamin; Nishimura, Nobuya; Subramanya, Vijay; Suzuki, Akira; Vaidyanathan, K. Ranji

doi:10.48550/arxiv.1803.06074

Cited by 1 publication

(2 citation statements)

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“…Although we are the first to consider the reconfiguration of minors, several papers have considered the reconfiguration of subgraphs [5,10]. The representation of a configuration as a labeling of the vertices has been used for problems entailing moving labels from a source to a target configuration using the minimum number of swaps, where labels (or tokens) on adjacent vertices can be exchanged (detailed in a survey of reconfiguration [11]), and labeled edges have been considered in the reconfiguring of triangulations [8].…”

Section: :2mentioning

confidence: 99%

“…Throughout the paper, we required every vertex of G to be a member of a branch set in an H-model. If instead we considered a subgraph of G, a solution might entail the labeling of a subset of the vertices of G. We observe that when the number of labels is equal to the number of vertices in H, the problem is reduced subgraph isomorphism [5]. Alternative mappings can be considered as well, such as topological embedding of one graph in another.…”

Section: Conclusion and Open Questionsmentioning

confidence: 99%

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Reconfiguration of graph minors

Moore¹,

Nishimura²,

Subramanya³

2018

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Under the reconfiguration framework, we consider the various ways that a target graph H is a minor of a host graph G, where a subgraph of G can be transformed into H by means of edge contraction (replacement of both endpoints of an edge by a new vertex adjacent to any vertex adjacent to either endpoint). Equivalently, an H-model of G is a labeling of the vertices of G with the vertices of H, where the contraction of all edges between identically-labeled vertices results in a graph containing representations of all edges in H.We explore the properties of G and H that result in a connected reconfiguration graph, in which nodes represent H-models and two nodes are adjacent if their corresponding H-models differ by the label of a single vertex of G. Various operations on G or H are shown to preserve connectivity. In addition, we demonstrate properties of graphs G that result in connectivity for the target graphs K 2 , K 3 , and K 4 , including a full characterization of graphs G that result in connectivity for K 2 -models, as well as the relationship between connectivity of G and other H-models.

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