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- W2901296759 abstract "We study decomposition into simple arcs (i. e., arcs without self-intersections) for diagrams of knots and spatial graphs. In this paper, it is proved in particular that if no edge of a finite spatial graph $G$ is a knotted loop, then there exists a plane diagram $D$ of $G$ such that (i) each edge of $G$ is represented by a simple arc of $D$ and (ii) each vertex of $G$ is represented by a point on the boundary of the convex hull of $D$. This generalizes the conjecture of S. Jablan and L. Radovi'{c} stating that each knot has a meander diagram, i. e., a diagram composed of two simple arcs whose common endpoints lie on the boundary of the convex hull of the diagram. Also, we prove another conjecture of Jablan and Radovi'{c} stating that each 2-bridge knot has a semi-meander minimal diagram, i. e., a minimal diagram composed of two simple arcs." @default.
- W2901296759 created "2018-11-29" @default.
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- W2901296759 date "2018-03-28" @default.
- W2901296759 modified "2023-09-27" @default.
- W2901296759 title "Meander diagrams of knots and spatial graphs: proofs of generalized Jablan--Radovi'{c} conjectures" @default.
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