Knotted Hamiltonian cycles in spatial embeddings of complete graphs
نویسندگان
چکیده
We show the complete graph on n vertices contains a knotted Hamiltonian cycle in every spatial embedding, for n > 7. Moreover, we show that for n > 8, the minimum number of knotted Hamiltonian cycles in every embedding of Kn is at least (n−1)(n−2) . . . (9)(8). We also prove K8 contains at least 3 knotted Hamiltonian cycles in every spatial embedding.
منابع مشابه
On cycles in intersection graphs of rings
Let $R$ be a commutative ring with non-zero identity. We describe all $C_3$- and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. Also, we shall describe all complete, regular and $n$-claw-free intersection graphs. Finally, we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. ...
متن کاملAn Algorithm for Detecting Intrinsically Knotted Graphs
We describe an algorithm that recognizes seemingly most — possibly all — intrinsically knotted (IK) graphs, and can help find knotless embeddings for graphs that are not IK. The algorithm, implemented as a Mathematica program, has already been used in [6] to greatly expand the list of known minor minimal IK graphs, and to find knotless embeddings for some graphs that had previously resisted att...
متن کاملOn strongly almost trivial embeddings of graphs
An algorithm for detecting intrinsically knotted graphs, yielding many new minor minimal IK graphs. Ramin Naimi Occidental College We describe an algorithm that detects seemingly most (and possibly all) intrinsically knotted (IK) graphs, and can help find knotless embeddings for graphs that are not IK. We have used this algorithm, implemented as a Mathematica program, to find many new minor min...
متن کاملThe 3-move and Knotted 4-valent Graphs in 3-space
A topological graph is a one-dimensional complex consisting of finitely many 0-cells (vertices) and finitely many 1-cells (edges and loops). In [7], Kauffman proved that piecewise linear ambient isotopy of a piecewise linear embedding of a topological graph in Euclidean 3-space R3 or 3-sphere 3, referred simply a knotted graph, is generated by a set of diagrammatic local moves (see Fig. 1) that...
متن کاملA Linear Time Algorithm for Visualizing Knotted Structures in 3 Pages
We introduce simple codes and fast visualization tools for knotted structures in molecules and neural networks. Knots, links and more general knotted graphs are studied up to an ambient isotopy in Euclidean 3-space. A knotted graph can be represented by a plane diagram or by an abstract Gauss code. First we recognize in linear time if an abstract Gauss code represents an actual graph embedded i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007