Intrinsic Properties of Spatial Graphs - Denison University

Introduction Linking and Knotting Other Intrinsic Properties ConclusionIntrinsically composite?Given a knot K , let p(K ) be the minimal number of factors in adecomposition of the knot into a connected sum of prime knots.Are their graphs for which every embedding has a knot withlarge p(K )? No!Theorem (Flapan, Howards, 2009)Every graph has an embedding in which every knotted cycle isa hyperbolic knot.Since all hyperbolic knots are prime, this means every graphhas an embedding in which all knots are prime knots, withp(K ) = 1.Blake MellorIntrinsic Properties of Spatial Graphs