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.
@InProceedings{moore_et_al:LIPIcs.MFCS.2018.75, author = {Moore, Benjamin and Nishimura, Naomi and Subramanya, Vijay}, title = {{Reconfiguration of Graph Minors}}, booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)}, pages = {75:1--75:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-086-6}, ISSN = {1868-8969}, year = {2018}, volume = {117}, editor = {Potapov, Igor and Spirakis, Paul and Worrell, James}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.75}, URN = {urn:nbn:de:0030-drops-96573}, doi = {10.4230/LIPIcs.MFCS.2018.75}, annote = {Keywords: reconfiguration, graph minors, graph algorithms} }
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