Zobrazeno 1 - 10
of 84
pro vyhledávání: '"Sedgwick, Eric"'
Publikováno v:
Discrete and Computational Geometry 72 (2024), no. 1, 246-268
For every $n$, we construct two curves in the plane that intersect at least $n$ times and do not form spirals. The construction is in three stages: we first exhibit closed curves on the torus that do not form double spirals, then arcs on the torus th
Externí odkaz:
http://arxiv.org/abs/2206.07849
Autor:
Burton, Benjamin A., Chang, Hsien-Chih, Löffler, Maarten, de Mesmay, Arnaud, Maria, Clément, Schleimer, Saul, Sedgwick, Eric, Spreer, Jonathan
We present three "hard" diagrams of the unknot. They require (at least) three extra crossings before they can be simplified to the trivial unknot diagram via Reidemeister moves in $\mathbb{S}^2$. Both examples are constructed by applying previously p
Externí odkaz:
http://arxiv.org/abs/2104.14076
We show that determining the crossing number of a link is NP-hard. For some weaker notions of link equivalence, we also show NP-completeness.
Externí odkaz:
http://arxiv.org/abs/1908.04073
We prove that deciding if a diagram of the unknot can be untangled using at most $k$ Riedemeister moves (where $k$ is part of the input) is NP-hard. We also prove that several natural questions regarding links in the $3$-sphere are NP-hard, including
Externí odkaz:
http://arxiv.org/abs/1810.03502
We show that a small tree-decomposition of a knot diagram induces a small sphere-decomposition of the corresponding knot. This, in turn, implies that the knot admits a small essential planar meridional surface or a small bridge sphere. We use this to
Externí odkaz:
http://arxiv.org/abs/1809.02172
We prove that the problem of deciding whether a 2- or 3-dimensional simplicial complex embeds into $\mathbb{R}^3$ is NP-hard. Our construction also shows that deciding whether a 3-manifold with boundary tori admits an $\mathbb{S}^{3}$ filling is NP-h
Externí odkaz:
http://arxiv.org/abs/1708.07734
We show that {\sc Heegaard Genus $\leq g$}, the problem of deciding whether a triangulated 3-manifold admits a Heegaard splitting of genus less than or equal to $g$, is NP-hard. The result follows from a quadratic time reduction of the NP-complete pr
Externí odkaz:
http://arxiv.org/abs/1606.01553
Publikováno v:
In Advances in Mathematics 16 April 2021 381
Publikováno v:
Pacific J. Math. 292 (2018) 257-272
A topologically minimal surface may be isotoped into a normal form with respect to a fixed triangulation. If the intersection with each tetrahedron is simply connected, then the pieces of this normal form are triangles, quadrilaterals, and helicoids.
Externí odkaz:
http://arxiv.org/abs/1502.05646
Publikováno v:
Discrete & Computational Geometry; Jul2024, Vol. 72 Issue 1, p246-268, 23p