Print Email Facebook Twitter Graph MBO on Star Graphs and Regular Trees. Title Graph MBO on Star Graphs and Regular Trees.: With Corrections to DOI 10.1007/s00032-014-0216-8 Author van Gennip, Y. (TU Delft Mathematical Physics) Date 2019 Abstract The graph Merriman–Bence–Osher scheme produces, starting from an initial node subset, a sequence of node sets obtained by iteratively applying graph diffusion and thresholding to the characteristic (or indicator) function of the node subsets. One result in [14] gives sufficient conditions on the diffusion time to ensure that the set membership of a given node changes in one iteration of the scheme. In particular, these conditions only depend on local information at the node (information about neighbors and neighbors of neighbors of the node in question). In this paper we show that there does not exist any graph which satisfies these conditions. To make up for this negative result, this paper also presents positive results regarding the Merriman–Bence–Osher dynamics on star graphs and regular trees. In particular, we present sufficient (and in some cases necessary) results for the set membership of a given node to change in one iteration. Subject graph dynamicsMerriman–Bence–Osher schemeregular tree graphstar graphthreshold dynamics To reference this document use: http://resolver.tudelft.nl/uuid:e4fb0f1e-a729-4680-aa3d-aa71b2029bc5 DOI https://doi.org/10.1007/s00032-019-00296-1 ISSN 1424-9286 Source Milan Journal of Mathematics, 87 (1), 141-168 Part of collection Institutional Repository Document type journal article Rights © 2019 Y. van Gennip Files PDF 10.1007_s00032_019_00296_1.pdf 1.73 MB Close viewer /islandora/object/uuid:e4fb0f1e-a729-4680-aa3d-aa71b2029bc5/datastream/OBJ/view