Reconfiguration of Graph Minors

Authors Benjamin Moore, Naomi Nishimura, Vijay Subramanya

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Benjamin Moore
  • Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada
Naomi Nishimura
  • David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada
Vijay Subramanya
  • David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada

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Benjamin Moore, Naomi Nishimura, and Vijay Subramanya. Reconfiguration of Graph Minors. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 75:1-75:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
  • reconfiguration
  • graph minors
  • graph algorithms


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