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Factoring polynomials with rational coefficients
In this paper we present a polynomial-time algorithm to solve the following problem: given a non-zero polynomial fe Q(X) in one variable with rational coefficients, find the decomposition of f intoExpand
Geometric Algorithms and Combinatorial Optimization
0. Mathematical Preliminaries.- 0.1 Linear Algebra and Linear Programming.- Basic Notation.- Hulls, Independence, Dimension.- Eigenvalues, Positive Definite Matrices.- Vector Norms, Balls.- MatrixExpand
On the Shannon capacity of a graph
  • L. Lovász
  • Mathematics, Computer Science
  • IEEE Trans. Inf. Theory
  • 1979
TLDR
It is proved that the Shannon zero-error capacity of the pentagon is \sqrt{5} and a well-characterized, and in a sense easily computable, function is introduced which bounds the capacity from above and equals the capacity in a large number of cases. Expand
Cones of Matrices and Set-Functions and 0-1 Optimization
A system, method, and apparatus for facilitating a self-organizing workforce of one or more workers through payment and recognition incentives, a set of configurable operating rules, and a set ofExpand
The ellipsoid method and its consequences in combinatorial optimization
TLDR
The method yields polynomial algorithms for vertex packing in perfect graphs, for the matching and matroid intersection problems, for optimum covering of directed cuts of a digraph, and for the minimum value of a submodular set function. Expand
Limits of dense graph sequences
We show that if a sequence of dense graphs G"n has the property that for every fixed graph F, the density of copies of F in G"n tends to a limit, then there is a natural ''limit object,'' namely aExpand
Combinatorial problems and exercises
Problems Hints Solutions Dictionary of the combinatorial phrases and concepts used Notation Index of the abbreviations of textbooks and monographs Subject index Author index Errata.
Submodular functions and convexity
TLDR
In “continuous” optimization convex functions play a central role, and linear programming may be viewed as the optimization of very special (linear) objective functions over very special convex domains (polyhedra). Expand
Kneser's Conjecture, Chromatic Number, and Homotopy
  • L. Lovász
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 1 November 1978
Abstract If the simplicial complex formed by the neighborhoods of points of a graph is (k − 2)-connected then the graph is not k-colorable. As a corollary Kneser's conjecture is proved, assertingExpand
On the ratio of optimal integral and fractional covers
  • L. Lovász
  • Computer Science, Mathematics
  • Discret. Math.
  • 1975
It is shown that the ratio of optimal integral and fractional covers of a hypergraph does not exceed 1 + log d, where d is the maximum degree. This theorem may replace probabilistic methods inExpand
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