Journal ArticleDOI
Knots and links in spatial graphs
John H. Conway,C. McA. Gordon +1 more
TLDR
It is shown that any embedding of K7 in three-dimensional euclidean space contains a knotted cycle and that any embedded cycle of K6 contains a pair of disjoint cycles which are homologically linked.Abstract:
The main purpose of this paper is to show that any embedding of K7 in three-dimensional euclidean space contains a knotted cycle. By a similar but simpler argument, it is also shown that any embedding of K6 contains a pair of disjoint cycles which are homologically linked.read more
Citations
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Journal ArticleDOI
The NP-completeness column: An ongoing guide
TL;DR: This is the fourteenth edition of a quarterly column that provides continuing coverage of new developments in the theory of NP-completeness, and readers who have results they would like mentioned (NP-hardness, PSPACE- hardness, polynomialtime-solvability, etc.), or open problems they wouldlike publicized, should send them to David S. Johnson.
Book
Introduction to the theory of complexity
TL;DR: 1. Mathematical Preliminaries, Elements of Computability Theory, and Space-Complexity Classes: Algorithms and Complexity Classes.
Journal ArticleDOI
Invariants of graphs in three-space
TL;DR: In this paper, a collection de nœuds et d'aretes a un graphe dans un espace tridimensionnel, on obtient des invariants calculables du type de plongement du graphe.
Journal ArticleDOI
Nonconstructive tools for proving polynomial-time decidability
TL;DR: New methods are employed to prove membership in P for a number of problems whose complexities are not otherwise known and their utility is illustrated.
Journal ArticleDOI
An Extended Simple Power Consumption Model for Selecting a Server to Perform Computation Type Processes in Digital Ecosystems
TL;DR: An improved power consumption laxity-based (IPCLB) algorithm for selecting a server is proposed in this paper, where the minimum power to be consumed is used to perform the process.
References
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Book ChapterDOI
An enumeration of knots and links, and some of their algebraic properties
TL;DR: In this article, the authors describe knots and links and some of their algebraic properties, and show that any knot diagram can be obtained by substituting algebraic tangles for the vertices of some basic polyhedron P in fact P, and the manner of substitution is essentially unique.
Journal ArticleDOI
Untersuchungen über quadratische Formen in Körpern der Charakteristik 2. (Teil I.).
TL;DR: In this paper, Hasse et al. untersuchen in W. Q. den dort nicht betrachteten Fall untersuchhen, daß k die Charakteristik 2 hat.
Journal ArticleDOI
The conway polynomial
TL;DR: In this article, the authors give an exposition of the Conway polynomial, and explain the source of its properties by modelling it in analogy to the Alexander polynomials via the potential function V(x x-