Permanents , Pfaffian orientations , and even directed circuits

  title={Permanents , Pfaffian orientations , and even directed circuits},
  author={Neil Robertson and Paul D. Seymour and Robin Thomas},
Given a 0-1 square matrix A, when can some of the 1’s be changed to −1’s in such a way that the permanent of A equals the determinant of the modified matrix? When does a real square matrix have the property that every real matrix with the same sign pattern (that is, the corresponding entries either have the same sign or are both zero) is nonsingular? When is a hypergraph with n vertices and n hyperedges minimally nonbipartite? When does a bipartite graph have a “Pfaffian orientation”? Given a… CONTINUE READING


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Publications referenced by this paper.
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Aufgabe 424

  • G. Pólya
  • Arch. Math. Phys. Ser. 20
  • 1913
Highly Influential
11 Excerpts

A characterization of convertible (0

  • C.H.C. Little
  • 1)-matrices, J. Combinatorial Theory 18
  • 1975
Highly Influential
6 Excerpts

Dimer statistics and phase transitions

  • P. W. Kasteleyn
  • J. Mathematical Phys. 4
  • 1963
Highly Influential
5 Excerpts


  • W. McCuaig, N. Robertson, P. D. Seymour, R. Thomas
  • Pfaffian orientations, and even directed circuits
  • 1997
1 Excerpt

Matrices of Sign-Solvable Linear Systems

  • R. A. Brualdi, B. L. Shader
  • Cambridge Tracts in Math. 116, Cambridge Univ…
  • 1995
1 Excerpt

Operations preserving the Pfaffian property of a graph

  • C.H.C. Little, F. Rendl
  • J. Austral. Math. Soc. 50
  • 1991

Matching Theory

  • L. Lovász, M. Plummer
  • Ann. of Discrete Math. 29, North-Holland, New…
  • 1986
2 Excerpts

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