Intrinsic Properties of Spatial Graphs - Denison University
Intrinsic Properties of Spatial Graphs - Denison University
Intrinsic Properties of Spatial Graphs - Denison University
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Introduction Linking and Knotting Other <strong>Intrinsic</strong> <strong>Properties</strong> ConclusionStraight-edge EmbeddingsIn a straight-edge embedding, every edge is embedded as astraight line.Theorem (Negami, 1991)Given a link L, there is a number R(L) such that whenevern ≥ R(L), every straight-edge embedding <strong>of</strong> K n contains a linkequivalent to L.Which links can be realized in straight-edge embeddings <strong>of</strong>particular graphs?Hughes* (2007) and Huh and Jeon (2008) proved that everystraight-edge embedding <strong>of</strong> K 6 has one or three pairs <strong>of</strong> linkedtriangles; Ludwig and Arbisi* (2010) investigated links in K 7 .Blake Mellor<strong>Intrinsic</strong> <strong>Properties</strong> <strong>of</strong> <strong>Spatial</strong> <strong>Graphs</strong>
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