Biography

List of Publications

Autobiographical Notes

Geometry

On the Foundations of Inversion Geometry, Trans. Amer. Math. Soc. 17 (1951) 218-242

Cyclic Affine Planes, Can. J. Math. 4 (1952) 295-301

(with M. Newman, E. G. Straus and O. Taussky) On the Number of Absolute Points of a Correlation, Pacific J. Math. 6 (1956) 83-96

On Unions and Intersections of Cones, in 1969 Recent Progress in Combinatorics, Proc. Third Waterloo Conf. on Combinatorics 1968, pp. 103-109

Binding Constraints and Helly Numbers, in Second Int. Conf. on Combinatorial Mathematics (New York, 1978), pp. 284-288, Ann,. New York Acad. Sci. 319 (1979)

Combinatorics

(with P.C. Gilmore) A Characterization of Comparability Graphs and of Interval Graphs, Can. J. Math. 16 (1964) 539-548

(with D.R. Fulkerson ami M. II. McAndrew) Some Properties of Graphs with Multiple Edges, Can. J. Math. 17 (1965) 166-177

(with R.K. Brayton and Don Coppersmith) Self orthogonal Latin Squares, in Colloquio Int. sulle Teorie Combinatorie (Rome, 1973), Tomo II, 509-517, Atti dei Convegni Lincei, No. 17, Accad. Naz. Lincei, Rome, 1976

(with D.E. Schwartz) On Partitions of a Partially Ordered Set, J. Comb. Theory Ser. B 23 (1977) 3-13

(with Dasong Cao, V. Chvátal and A. Vince) Variations on a Theorem of Ryser, Linear Algebra Appl. 260 (1997) 215-222

Matrix Inequalities and Eigenvalues

(with H. W. Wielandt) The Variation of the Spectrum of a Normal Matrix, Duke Matfa. J. 20 (1953) 37-39

(with Ky Fan) Some Metric Inequalities in the Space of Matrices, Proc. Amer. Math. Soc. 6 (1955) 111-116

(with Paul Camion) On the Nonsingularity of Complex Matrices, Pacific J. Math. 17 (1966) 211-214

Combinatorial Aspects of Gerschgorin's Theorem, in 1971 Recent Trends in Graph Theory (Proc. Conf., New York, 1970), pp. 173-179, Lecture Notes in Mathematics 186

Linear G-functions, Linear and Multilinear Algebra 3 (1975) 45-52

(with Jean-Louis Coffin) On the Relationship Between the Hausdorff Distance and Matrix Distances of Ellipsoids, Linear Algebra Appl. 52/53 (1983) 301-313

(with E. R. Barnes) Bounds for the Spectrum of Normal Matrices, Linear Algebra Appt. 201 (1994) 79-90

Linear Inequalities and Linear Programming

On Approximate Solutions of Systems of Linear Inequalities, J. Res. Natl. Bureau Stds. 49 (1952) 263-265

Cycling in the Simplex Algorithm, Natl. Bureau Stds. Rep. 2974 (1953)

(with M. Mannos, D. Sokolowsky and N. Wiegmann) Computational Experience in Solving Linear Programs, J. Soc. Indust. Appl. Math. 1 (1953) 17-33

On Abstract Dual Linear Programs, Naval Res. Logistics Quart. 10 (1963) 369-373

(with Uriel G. Rothblum) A Proof of the Convexity of the Range of a Nonatomic Vector Measure Using Linear Inequalities, Linear Algebra Appl. 199 (1994) 373-379

(with E.V. Denardo, T. Mackenzie and W.R. Pulleyblank) A Nonlinear Allocation Problem, IBM J. Res. Develop. 38 (1994) 301-306

Combinatorial Optimization

(with J.B. Kruskat) Integral Boundary Points of Convex Polyhedra, in Linear Inequalities and Related Systems, Ann. Math. Studies 38 (1956) 223-246

Some Recent Applications of the Theory of Linear Inequalities to Extremal Combinatorial Analysis, in 1960 Proc. Symp. Appl. Math. 10 (1960) 113-127

(with S. Winograd) Finding all Shortest Distances in a Directed Network, IBM J. Res. Develop. 16 (1972) 412-414

(with D. R. Fulkerson and Rosa Oppenheim) On Balanced Matrices, Math. Programming Study 1 (1974) 120-132

A Generalization of Max Flow-Min Cut, Math. Programming 6 (1974) 352-359

On Lattice Polyhedra III: Blockers and Anti-Blockers of Lattice Clutters, Math. Programming Study 8 (1978) 197-207

(with Rosa Oppenheim) Local Unimodularity in the Matching Polytope, Ann. Discrete Math. 2 (1978) 201-209

(with S. Thomas McCormick) A Fast Algorithm that Makes Matrices Optimally Sparse, in Prog. Combinatorial Optimization (Waterloo, Ont. 1982) 185-196

Greedy Algorithms

On Simple Linear Programming Problems, in 1963 Proc. Symp. Pure Math. VII (1963) 317-327

(with A.W.J. Kolen and M. Sakarovitch) Totally Balanced and Greedy Matrices, SIAM J. Algebraic Discrete Methods 6 (1985) 721-730

(with Alan C. Tucker) Greedy Packing and Series-Parallel Graphs, J. Comb. Theory Ser. A 47 (1988) 6-15

On Simple Combinatorial Optimization Problems, Discrete Math. 106/107 (1992) 285-289

(with Wolfgang W. Bein and Peter Brucker) Series Parallel Composition of Greedy Linear Programming Problems, Math. Programming 62 (1993) 114-

Graph Spectra

On the Uniqueness of the Triangular Association Scheine, Arm. Math. Statist. 31 (1960) 492-497

(with R.R. Singleton) Or Moore Graphs with Diameters 2 and 3, IBM J. Res. Develop. 4 (1960) 497-504

On the Polynomial of a Graph, Amer. Math. Monthly 70 (1963) 30-36

(with D.K. Ray-Chaudhari) On the Lille Graph of a Symmetric Balanced Incomplete Block Design, Trans. Amer. Math. Soc. 116 (1965) 238-252

On Eigenvalues and Colorings of Graphs, in Graph Theory and Its Applications, pp. 79-91

Eigenvalues and Partitionings of the Edges of a Graph, Linear Algebra Appl. 5 (1972) 137-146

On Spectrally Bounded Graphs, in A Survey of Combinatorial Theory (Colorado State Univ., Fort Collins, Colo. 1971), pp. 277-283

(with W.E. Donath) Lower Bounds for the Partitioning of Graphs, IBM J. Res. Develop. 17 (1973) 420-425

(with Peter Joffe) Nearest 8-Matrices of Given Rank and the Ramsey Problem for Eigenvalues of Bipartite 8-Graphs, in Colloq. Int. C.N.R.S. 260, Problèmes Combinatoire et Théore des Graphes, Univ. Orsay, Orsay, 1976, pp. 237-240