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Polyhedral Combinatorics
Edited by: William Cook and Paul D. Seymour
A co-publication of the AMS, DIMACS, and Association for Computing Machinery.
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DIMACS: Series in Discrete Mathematics and Theoretical Computer Science
1990; 288 pp; hardcover
Volume: 1
ISBN-10: 0-8218-6591-9
ISBN-13: 978-0-8218-6591-0
List Price: US$69
Member Price: US$55.20
Order Code: DIMACS/1
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This book, the first volume in the DIMACS book series, contains the proceedings of the first DIMACS workshop. The workshop, which was held in June 1989 in Morristown, New Jersey, focused on polyhedral combinatorics. Two series of lectures were presented by L. Lovász and A. Schrijver and there were a number of shorter lectures. The topics covered include multicommodity flows, graph matchings and colorings, the traveling salesman problem, integer programming, and complexity theory. Aimed at researchers in combinatorics and combinatorial optimization, this book will provide readers with an overview of recent advances in combinatorial optimization.

Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM).

Table of Contents

  • L. Lovász and A. Schrijver -- Matrix cones, projection representations, and stable set polyhedra
  • G. Narasimhan and R. Manber -- A generalization of Lovász's \(\theta\) function
  • A. M. H. Gerards -- On cutting planes and matrices
  • M. E. Dyer, A. Füredi, and C. McDiarmid -- Random volumes in the \(n\)-cube
  • R. Kannan -- Test sets for integer programs, \(\forall \exists\) sentences
  • S. N. Kabadi and R. Chandrasekaran -- Solvable classes of generalized traveling salesman problems
  • D. Naddef -- Handles and teeth in the symmetric traveling salesman polytope
  • W. Cook and M. Hartmann -- On the complexity of branch and cut methods for the traveling salesman problem
  • K. Cameron and J. Edmonds -- Existentially polytime theorems
  • A. Lehman -- The width-length inequality and degenerate projective planes
  • P. D. Seymour -- On Lehman's width-length characterization
  • A. Schrijver -- Applications of polyhedral combinatorics to multicommodity flows and compact surfaces
  • A. Frank and A. Schrijver -- Vertex-disjoint simple paths of given homotopy in a planar graph
  • A. Frank -- On disjoint homotopic paths in the plane
  • M. Middendorf and F. Pfeiffer -- On the complexity of the disjoint paths problem (extended abstract)
  • M. Middendorf and F. Pfeiffer -- The paths-selection problem
  • F. Barahona -- Planar multicommodity flows, max cut, and the Chinese postman problem
  • A. Sebő -- The cographic multiflow problem: An epilogue
  • O. Marcotte -- Exact edge-colorings of graphs without prescribed minors
  • O. Marcotte -- On the chromatic index of multigraphs and a conjecture of Seymour, (II)
  • A. Schrijver and P. D. Seymour -- Spanning trees of different weights
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