Two Analogs of Intrinsically Linked Graphs - Mathematics > Geometric TopologyReport as inadecuate




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Abstract: A graph G is intrinsically S^1-linked if for every embedding of the verticesof G into S^1, vertices that form the endpoints of two disjoint edges in G forma non-split link in the embedding. We show that a graph is intrinsicallyS^1-linked if and only if it is not outer-planar. A graph is outer-flat if itcan be embedded in the 3-ball such that all of its vertices map to the boundaryof the 3-ball, all edges to the interior, and every cycle bounds a disk in the3-ball that meets the graph only along its boundary. We show that a graph isouter-flat if and only if it is planar.



Author: Chris Cicotta, Joel Foisy, Tom Reilly, Sara Revzi, Ben Wang, Alice Wilson

Source: https://arxiv.org/







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