Victor Klee

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All published works

Action	Title	Year	Authors
+	In a remarkable paper, Bishop and Phelps (1) settle several important questions concerning supporting hyperplanes of convex sets in Banach spaces. In particular, they show that if C is a closed convex subset of a Banach space	2016	Victor Klee
+	Basic properties of evenly convex sets	2007	Victor Klee Elisabetta Maluta Clemente Zanco
+	Computational Convexity	2004	Peter Gritzmann Victor Klee
+	Approximation of diameters: randomization doesn't help	2002	Andreas Brieden Peter Gritzmann Ravi Kannan Victor Klee László Lovász Miklós Simonovits
+	Deterministic and randomized polynomial‐time approximation of radii	2001	Andreas Brieden Peter Gritzmann Ravindran Kannan Victor Klee László Lovász Miklós Simonovits
+	Oracle-polynomial-time approximation of largest simplices in convex bodies	2000	Andreas Brieden Peter Gritzmann Victor Klee
+	Decomposition Theorems for Conditional Sign-Solvability and Sign-Solvability of General Systems	2000	Shawn Cokus Victor Klee
+	Inapproximability of some Geometric and Quadratic Optimization Problems	2000	Andreas Brieden Peter Gritzmann Victor Klee
+	Inner Diagonals of Convex Polytopes	1999	David Avis Victor Klee
+	Inner diagonals of convex polytopes.	1999	David Avis Victor Klee
+	A proof of the strict monotone 4-step conjecture	1999	Fred B. Holt Victor Klee
+ PDF Chat	Many Polytopes Meeting the Conjectured Hirsch Bound	1998	Fred B. Holt Victor Klee
+	A Surprising but Easily Proved Geometric Decomposition Theorem	1998	Victor Klee John R. Reay
+	A Surprising but Easily Proved Geometric Decomposition Theorem	1998	Victor Klee John R. Reay
+	Separation by hyperplanes in finite-dimensional vector spaces over Archimedean ordered fields.	1998	Peter Gritzmann Victor Klee
+ PDF Chat	Appollonius Revisited: Supporting Spheres for Sundered Systems	1997	Victor Klee Teresa Lewis Balder Von Hohenbalken
+	Alte und neue ungelöste Probleme in der Zahlentheorie und Geometrie der Ebene	1997	Victor Klee Stan Wagon
+	Zahlentheorie	1997	Victor Klee Stan Wagon
+	Zweidimensionale Geometrie	1997	Victor Klee Stan Wagon
+	Interessante reelle Zahlen	1997	Victor Klee Stan Wagon
+	Polytope Projection and Projection Polytopes	1996	Thomas Bürger Peter Gritzmann Victor Klee
+	Polytope Projection and Projection Polytopes	1996	Thomas Bürger Peter Gritzmann Victor Klee
+	Convex polytopes and related complexes	1996	Victor Klee Peter Kleinschmidt
+	Linear algebra, polytopes, and the hirsch conjecture	1996	Fredrick Baden Holt Victor Klee
+	Rotundity and smoothness of convex bodies in reflexive and nonreflexive spaces	1996	Victor Klee Libor Veselý Clemente Zanco
+	Cross-positive matrices revisited	1995	Peter Gritzmann Victor Klee Bit-Shun Tam
+ PDF Chat	Largestj-simplices inn-polytopes	1995	Peter Gritzmann Victor Klee D. G. Larman
+	Polytope Containment and Determination by Linear Probes	1995	Peter Gritzmann Victor Klee John Westwater
+	External Tangents and Closedness of Cone + Subspace	1994	Peter Gritzmann Victor Klee
+	On the Complexity of Some Basic Problems in Computational Convexity	1994	Peter Gritzmann Victor Klee
+	On the recognition of S-systems	1993	Victor Klee Balder Von Hohenbalken Ted G. Lewis
+	Archimedean levels, semispaces, and majorization of convex cones	1993	Victor Klee Elisabetta Maluta Clemente Zanco
+	Sharper approximation of extreme points by far points	1993	Victor Klee
+	Mathematical Programming and Convex Geometry	1993	Peter Gritzmann Victor Klee
+	Old and New Unsolved Problems in Plane Geometry and Number Theory.	1992	Paul R. Halmos Victor Klee Stan Wagon
+ PDF Chat	Inner and outerj-radii of convex bodies in finite-dimensional normed spaces	1992	Peter Gritzmann Victor Klee
+	Number Theory	1991	Victor Klee Stan Wagon
+	Old and New Unsolved Problems in Plane Geometry and Number Theory	1991	Victor Klee Stan Wagon
+	Good and Bad Radii of Convex Polygons	1991	Peter Gritzmann Laurent Habsieger Victor Klee
+	Uniform properties of collections of convex bodies	1991	Victor Klee Elisabetta Maluta Clemente Zanco
+ PDF Chat	Geometry of the Gass-Saaty parametric cost LP algorithm	1990	Victor Klee Peter Kleinschmidt
+ PDF Chat	Optimization of Globally Convex Functions	1989	T. C. Hu Victor Klee David Larman
+ PDF Chat	On the 0–1-Maximization of Positive Definite Quadratic Forms	1989	Peter Gritzmann Victor Klee
+	Sign-Patterns and Stability	1989	Victor Klee
+	Minimum graphs of specified diameter, connectivity and valence. II	1989	E. Engelhardt Victor Klee K. Li Howard Quaife
+	Recursive structure of S-matrices and an O(m2) algorithm for recognizing strong sign solvability	1987	Victor Klee
+	Limits of starshaped sets	1987	Gerald Beer Victor Klee
+	Inspheres and inner products	1986	Victor Klee Elisabetta Maluta Clemente Zanco
+	Banach Spaces and Hilbert Spaces	1986	Shizuo Kakutani Victor Klee Kôsaku Yosida Yukio Mimura H. F. Bohnenblust Masahiro Nakamura George W. Mackey Paul R. Halmos
+	Diameters of random bipartite graphs	1984	Béla Bollobás Victor Klee
+	A note on convex cones and constraint qualifications in infinite-dimensional vector spaces	1982	Victor Klee
+	Dispersed Chebyshev sets and coverings by balls	1981	Victor Klee
+ PDF Chat	Diameters of Random Graphs	1981	Victor Klee David Larman
+	Another generalization of Carath�odory's theorem	1980	Victor Klee
+	Some Unsolved Problems in Plane Geometry	1979	Victor Klee
+	Some Unsolved Problems in Plane Geometry	1979	Victor Klee
+	Adjoints of projective transformations and face-figures of convex polytopes	1978	Victor Klee
+	A linearly compact convex set dense in every vector topology	1977	Victor Klee
+	Linear algorithms for testing the sign stability of a matrix and for findingZ-maximum matchings in acyclic graphs	1977	Victor Klee P. van den Driessche
+	Classification and enumeration of minimum (d, 1, 3)-graphs and minimum (d, 2, 3)-graphs	1977	Victor Klee Howard Quaife
+	Impressions of Mathematical Education in the People's Republic of China	1977	Victor Klee
+	Impressions of Mathematical Education in the People's Republic of China	1977	Victor Klee
+	Adjoints of Projective Transformations and Face-Figures of Convex Polytopes	1976	Victor Klee
+	Minimum Graphs of Specified Diameter, Connectivity and Valence. I	1976	Victor Klee Howard Quaife
+ PDF Chat	Unique reducibility of subsets of commutative topological groups and semigroups.	1975	David Gale Victor Klee
+	Spira's theorems on complete linear proofs of systems of linear inequalities	1975	Victor Klee
+	Minimum graphs of specified diameter, connectivity and valence	1975	Victor Klee Howard Quaife
+	Ratio-sequences of chains in connected metric spaces	1975	Victor Klee
+	Shellings of spheres and polytopes	1974	Gopal Danaraj Victor Klee
+ PDF Chat	Polytope pairs and their relationship to linear programming	1974	Victor Klee
+	Some Proximate Concepts in Topology.	1973	Victor Klee André L. Yandl
+ PDF Chat	On a Question of Colin Clark Concerning Three Properties of Convex Sets<sup>(1)</sup>	1972	Victor Klee
+	Convexity and Optimization in Finite Dimension (Josef Stoer and Christoph Witzgall)	1972	Victor Klee
+	Unions of increasing and intersections of decreasing sequences of convex sets	1972	Victor Klee
+	Semicontinuity of the face-function of a convex set	1971	Victor Klee Michael A. Martin
+	What Is a Convex Set?	1971	Victor Klee
+	HOW GOOD IS THE SIMPLEX ALGORITHM	1970	Victor Klee George J. Minty
+	On a lemma of fullerton and braunschweiger	1969	Victor Klee
+ PDF Chat	Intersection Theorems for Positive Sets	1969	Wolfhard Hansen Victor Klee
+	Invertibly positive linear operators on spaces of continuous functions	1969	Thomas A. Brown M. Juncosa Victor Klee
+	Can All Convex Borel Sets Be Generated in a Borelian Manner Within the Realm of Convexity?	1969	Victor Klee
+	Can All Convex Borel Sets be Generated in a Borelian Manner Within the Realm of Convexity?	1969	Victor Klee
+	Can the Boundary of a <i>d</i>-Dimensional Convex Body Contain Segments in all Directions?	1969	Victor Klee
+	Can the Boundary of a d-Dimensional Convex Body Contain Segments in All Directions?	1969	Victor Klee
+	What is the Expected Volume of a Simplex Whose Vertices are Chosen at Random from a Given Convex Body?	1969	Victor Klee
+	Is there an <i>n</i> for which φ(<i>x</i>)=<i>n</i> has a Unique Solution?	1969	Victor Klee
+	What is the Expected Volume of a Simplex Whose Vertices are Chosen at Random from a Given Convex Body?	1969	Victor Klee
+	Is There an n for which φ(x) = n Has a Unique Solution?	1969	Victor Klee
+	Can Nine Tetrahedra Form a Neighboring Family?	1969	Victor Klee
+	Is Every Polygonal Region Illuminable from Some Point?	1969	Victor Klee
+	Can Nine Tetrahedra Form a Neighboring Family?	1969	Victor Klee
+	Correction to "Summability in $ł(p_{1},p_{2},...)$ spaces" Studia Mathematica 25 (1965), p. 277-280)	1969	Victor Klee
+ PDF Chat	Intersection theorems for positive sets	1969	Wolfhard Hansen Victor Klee
+	Can a Plane Convex Body have Two Equichordal Points?	1969	Victor Klee
+	Can a Plane Convex Body have Two Equichordal Points?	1969	Victor Klee
+ PDF Chat	Maximal Separation Theorems for Convex Sets	1968	Victor Klee
+ PDF Chat	Convex functions on convex polytopes	1968	David Gale Victor Klee R. T. Rockafellar
+ PDF Chat	Maximal separation theorems for convex sets	1968	Victor Klee
+ PDF Chat	Asymptotes of Convex Bodies.	1967	Victor Klee
+	A comparison of primal and dual methods of linear programming	1966	Victor Klee
+ PDF Chat	Paths on polyhedra. II	1966	Victor Klee
+ PDF Chat	Exposed points of convex sets	1966	Gustave Choquet H. H. Corson Victor Klee
+	Every non-normable Frechet space is homeomorphic with all of its closed convex bodies	1966	C. Bessaga Victor Klee
+	PROBLEM SIZE IN LINEAR PROGRAMMING	1966	Victor Klee
+	Combinatorial Geometry in the Plane.	1965	G. P. Johnson H. Hadwiger Hans Debrunner Victor Klee
+	Paths on Polyhedra. I	1965	Victor Klee
+	A class of linear programming problems requiring a large number of iterations	1965	Victor Klee
+	A theorem on convex kernels	1965	Victor Klee
+ PDF Chat	Summability in $ł(p_{1},p_{2},...)$ spaces	1965	Victor Klee
+	Heights of convex polytopes	1965	Victor Klee
+	Dantzig's Simplex Method: <i>Linear Programming and Extensions</i> . George B. Dantzig. Princeton University Press, Princeton, N.J., 1963. xviii + 625 pp. Illus. $11.50.	1964	Victor Klee
+	Two topological properties of topological linear spaces	1964	C. Bessaga Victor Klee
+	Some semicontinuity theorems for convex polytopes and cell-complexes	1964	H. G. Eggleston Branko Grünbaum Victor Klee
+	A CLASS OF LINEAR PROGRAMMING PROBLEMS REQUIRING A LARGE NUMBER OF ITERATIONS	1964	Victor Klee
+	Utility functions and the ‘lin’ operation for convex sets	1964	Victor Klee
+	Extreme points of convex sets without completeness of the Scalar field	1964	Victor Klee
+	Connectedness in topological linear spaces	1964	Victor Klee
+ PDF Chat	On the Number of Vertices of a Convex Polytope	1964	Victor Klee
+ PDF Chat	A Combinatorial Analogue of Poincaré's Duality Theorem	1964	Victor Klee
+	Every Simple Closed Curve in E<sup>3</sup> is Unknotted in E<sup>4</sup>	1964	R. H. Bing Victor Klee
+	Diameters of Polyhedral Graphs	1964	Victor Klee
+	The finite topology of a linear space	1963	Shizuo Kakutani Victor Klee
+	On a theorem of Dubins	1963	Victor Klee
+	Combinatorial Mathematics. Herbert John Ryser. Published for the Mathematical Association of America by Wiley, New York, 1963. xiv + 154 pp. Illus. $4	1963	Victor Klee
+	Carus Mathematical Series: <i>Combinatorial Mathematics</i> . Herbert John Ryser. Published for the Mathematical Association of America by Wiley, New York, 1963. xiv + 154 pp. Illus. $4.	1963	Victor Klee
+	Carus Mathematical Series: <i>Combinatorial Mathematics</i> . Herbert John Ryser. Published for the Mathematical Association of America by Wiley, New York, 1963. xiv + 154 pp. Illus. $4.	1963	Victor Klee
+	ON THE NUMBER OF VERTICES OF A CONVEX POLYTOPE	1963	Victor Klee
+	The Euler Characteristic in Combinatorial Geometry	1963	Victor Klee
+	The Euler Characteristic in Combinatorial Geometry	1963	Victor Klee
+	Helly’s theorem and its relatives	1963	Ludwig Danzer Branko Grünbaum Victor Klee
+	Convexity	1963	Victor Klee
+ PDF Chat	Die innere Geometrie der metrischen Raume.	1962	Victor Klee Willi Rinow
+ PDF Chat	A Conjecture on Weak Compactness	1962	Victor Klee
+ PDF Chat	A conjecture on weak compactness	1962	Victor Klee
+	Exotic topologies for linear spaces	1962	Victor Klee
+	A Question of Katetov Concerning the Hilbert Parallelotope	1961	Victor Klee
+ PDF Chat	A question of Katětov concerning the Hilbert parallelotope	1961	Victor Klee
+ PDF Chat	Topological equivalence of a Banach space with its unit cell	1961	Victor Klee
+ PDF Chat	Stability of the fixed-point property	1961	Victor Klee
+ PDF Chat	Asymptotes and Projections of Convex Sets.	1960	Victor Klee
+	Shrinkable neighborhoods in Hausdorff linear spaces	1960	Victor Klee
+ PDF Chat	Mappings into normed linear spaces	1960	Victor Klee
+	Unsolved Problems in Intuitive Geometry	1960	Victor Klee
+ PDF Chat	Polyhedral sections of convex bodies	1960	Victor Klee
+	Some new results on smoothness and rotundity in normed linear spaces	1959	Victor Klee
+ PDF Chat	Some characterizations of convex polyhedra	1959	Victor Klee
+ PDF Chat	On the Borelian and Projective Types of Linear Subspaces.	1958	Victor Klee
+	On a problem of Banach	1958	Victor Klee
+	Homogeneity of Infinite-Dimensional Parallelotopes	1957	Victor Klee
+	On a method of mapping due to Kadeč and Bernstein	1957	Victor Klee Richard Long
+	A note on certain function spaces	1957	Mary Ellen Rudin Victor Klee
+	An example in the theory of topological linear spaces	1956	Victor Klee
+ PDF Chat	Iteration of the "lin" operation for convex sets	1956	Victor Klee
+	Fixed-Point Sets of Periodic Homeomorphisms of Hilbert Space	1956	Victor Klee
+ PDF Chat	Strict Separation of Convex Sets	1956	Victor Klee
+	Solution of a Problem of E. M. Wright on Convex Functions	1956	Victor Klee
+ PDF Chat	Strict separation of convex sets	1956	Victor Klee
+ PDF Chat	A note on topological properties of normed linear spaces	1956	Victor Klee
+	Boundedness and continuity of linear functionals	1955	Victor Klee
+ PDF Chat	Separation properties of convex cones	1955	Victor Klee
+ PDF Chat	Some Topological Properties of Convex Sets	1955	Victor Klee
+ PDF Chat	Common secants for plane convex sets	1954	Victor Klee
+ PDF Chat	Invariant extension of linear functionals	1954	Victor Klee
+ PDF Chat	A characterization of reflexivity by the lattice of closed subspaces	1954	E. E. Floyd Victor Klee
+	On a Theorem of Bela Sz.-Nagy	1953	Victor Klee
+ PDF Chat	Convex bodies and periodic homeomorphisms in Hilbert space	1953	Victor Klee
+	The Critical Set of a Convex Body	1953	Victor Klee
+ PDF Chat	Convex Bodies and Periodic Homeomorphisms in Hilbert Space	1953	Victor Klee
+ PDF Chat	Invariant metrics in groups (solution of a problem of Banach)	1952	Victor Klee
+ PDF Chat	Invariant Metrics in Groups (Solution of a Problem of Banach)	1952	Victor Klee
+ PDF Chat	On Certain Intersection Properties of Convex Sets	1951	Victor Klee
+	A Note on Fermat's Congruence	1949	Victor Klee
+	On a Problem of Erdos	1949	Victor Klee
+	A Generalization of Euler's φ-Function	1948	Victor Klee
+	Corrections: Some Remarks on Euler's Totient	1948	Victor Klee

Common Coauthors

Coauthor	Papers Together
Peter Gritzmann	17
Stan Wagon	7
Clemente Zanco	5
Andreas Brieden	4
Elisabetta Maluta	4
Howard Quaife	4
Branko Grünbaum	2
David Avis	2
Paul R. Halmos	2
C. Bessaga	2
Wolfhard Hansen	2
Balder Von Hohenbalken	2
Shizuo Kakutani	2
Peter Kleinschmidt	2
László Lovász	2
Thomas Bürger	2
Miklós Simonovits	2
David Gale	2
David Larman	2
Fred B. Holt	2
John R. Reay	2
H. G. Eggleston	1
G. P. Johnson	1
H. H. Corson	1
R. T. Rockafellar	1
P. van den Driessche	1
George W. Mackey	1
Yukio Mimura	1
E. E. Floyd	1
Ravindran Kannan	1
K. Li	1
D. G. Larman	1
Ravi Kannan	1
Masahiro Nakamura	1
H. Hadwiger	1
E. Engelhardt	1
R. H. Bing	1
Mary Ellen Rudin	1
Laurent Habsieger	1
Ludwig Danzer	1
Bit-Shun Tam	1
Kôsaku Yosida	1
Michael A. Martin	1
André L. Yandl	1
T. C. Hu	1
George J. Minty	1
Teresa Lewis	1
Ted G. Lewis	1
Fredrick Baden Holt	1
H. F. Bohnenblust	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Some characterizations of convex polyhedra	1959	Victor Klee	13
+ PDF Chat	Convex bodies and periodic homeomorphisms in Hilbert space	1953	Victor Klee	9
+	The maximum numbers of faces of a convex polytope	1970	Peter McMullen	9
+	Diameters of Polyhedral Graphs	1964	Victor Klee	8
+ PDF Chat	On the Number of Vertices of a Convex Polytope	1964	Victor Klee	8
+	Linear Programming and Extensions	1963	George B. Dantzig	8
+	Linear Programming and Extensions	1963	George B. Dantzig	8
+ PDF Chat	On The Number of Faces of a Convex Polytope	1964	David Gale	7
+ PDF Chat	Une remarque sur l'homéomorphie des champs fonctionnels	1929	S. Mazur	6
+ PDF Chat	Inner and outerj-radii of convex bodies in finite-dimensional normed spaces	1992	Peter Gritzmann Victor Klee	5
+ PDF Chat	Strict convexity and smoothness of normed spaces	1955	Mahlon M. Day	5
+ PDF Chat	An extension of Tietze’s theorem	1951	J. Dugundji	5
+	Neighborly and cyclic polytopes	1963	David Gale	5
+	Helly’s theorem and its relatives	1963	Ludwig Danzer Branko Grünbaum Victor Klee	5
+	Théorie des opérations linéaires	1932	Stefan Banach	5
+	The difference body of a convex body	1957	C. A. Rogers G. C. Shephard	4
+ PDF Chat	Uniformly convex spaces	1936	James A. Clarkson	4
+	Some semicontinuity theorems for convex polytopes and cell-complexes	1964	H. G. Eggleston Branko Grünbaum Victor Klee	4
+	Reflexivity and the Supremum of Linear Functionals	1957	Robert James	4
+ PDF Chat	A random polynomial-time algorithm for approximating the volume of convex bodies	1991	Martin Dyer Alan Frieze Ravi Kannan	4
+	Die Homoiomorphie der kompakten konvexen Mengen im Hilbertschen Raum	1931	Ott‐Heinrích Keller	4
+ PDF Chat	On the 0–1-Maximization of Positive Definite Quadratic Forms	1989	Peter Gritzmann Victor Klee	4
+	Letter to the Editor—A Conjecture Concerning the Smallest Bound on the Iterations in Linear Programming	1963	Thomas L. Saaty	4
+ PDF Chat	Separation properties of convex cones	1955	Victor Klee	4
+	Some new results on smoothness and rotundity in normed linear spaces	1959	Victor Klee	4
+	Polynomial algorithms in linear programming	1980	Leonid Khachiyan	4
+	Convex polytopes and the upper bound conjecture	1971	Peter McMullen G. C. Shephard J. E. Reeve Alan Ball	4
+ PDF Chat	Über die kleinste konvexe Menge, die eine gegebene kompakte Menge enthält	1930	S. Mazur	4
+	An enumeration of simplicial 4-polytopes with 8 vertices	1967	Branko Grünbaum V. P. Sreedharan	4
+	Graph-theoretical approach to qualitative solvability of linear systems	1982	Rachel Manber	4
+	Computing the volume of convex bodies: a case where randomness provably helps	1991	Martin Dyer Alan Frieze	3
+	Eulers Charakteristik und kombinatorische Geometrie.	1955	H. Hadwiger	3
+ PDF Chat	On the line segments of a convex surface in<i>E</i><sub>3</sub>	1960	Trevor McMinn	3
+ PDF Chat	Convex Bodies and Periodic Homeomorphisms in Hilbert Space	1953	Victor Klee	3
+	Scissor congruence	1963	Lester E. Dubins Morris W. Hirsch Jack Karush	3
+	Vorlesungen über die Theorie der Polyeder	1976	E. Steinitz H. Rademacher	3
+	Über Mengen konvexer Körper mit gemeinschaftlichen Punkte.	1923	Ed. Helly	3
+ PDF Chat	Simple paths on convex polyhedra	1961	Tom Brown	3
+	An Introduction to the Theory of Numbers. By G. H. Hardy and E. M. Wright. 2nd edition. Pp. xvi, 407 25s. 1945. (Oxford)	1946	T. A. A. B.	3
+ PDF Chat	Invariant Metrics in Groups (Solution of a Problem of Banach)	1952	Victor Klee	3
+	Finding the convex hull facet by facet	1985	Garret Swart	3
+	The Complexity of Vertex Enumeration Methods	1983	Martin Dyer	3
+ PDF Chat	On the decidability of Diophantine problems in combinatorial geometry	1987	Bernd Sturmfels	3
+	Heights of convex polytopes	1965	Victor Klee	3
+ PDF Chat	Topological properties of the unit sphere of a Hilbert space	1943	Shizuo Kakutani	3
+	The minimum number of vertices of a simple polytope	1971	David Barnette	3
+	The finite topology of a linear space	1963	Shizuo Kakutani Victor Klee	3
+ PDF Chat	Computing the volume is difficult	1987	Imre Bárány Zoltán Füredi	3
+	Qualitative Problems in Matrix Theory	1969	John Maybe J. P. Quirk	3
+	An Introduction to Convex Polytopes	1983	Arne Brøndsted	3