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Volumn 3, Issue , 2006, Pages 963-984

A survey of Pfaffian orientations of graphs

Author keywords

Brace; Brick; Crossing number; Dimer problem; Even directed cycle; Graph; Matching; Pfaffian orientation; P lya's permanent problem; Sign nonsingular matrix

Indexed keywords

BRACE; CROSSING NUMBER; DIMER PROBLEM; EVEN DIRECTED CYCLE; GRAPH; MATCHING; PFAFFIAN ORIENTATION; SIGN-NONSINGULAR MATRIX;

EID: 84878028194     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper
Times cited : (49)

References (65)
  • 1
    • 0002227678 scopus 로고
    • Restricted colorings of graphs
    • London Math. Soc. Lecture Note Ser. 187, Cambridge University Press, Cambridge
    • Alon, N., Restricted colorings of graphs. In Surveys in Combinatorics, London Math. Soc. Lecture Note Ser. 187, Cambridge University Press, Cambridge 1993, 1-33.
    • (1993) Surveys in Combinatorics , pp. 1-33
    • Alon, N.1
  • 2
    • 0000576339 scopus 로고
    • Colorings and orientations of graphs
    • Alon, N., and Tarsi, M., Colorings and orientations of graphs. Combinatorica 12 (1992), 125-134.
    • (1992) Combinatorica , vol.12 , pp. 125-134
    • Alon, N.1    Tarsi, M.2
  • 3
    • 0001336132 scopus 로고
    • Three observations on linear algebra
    • in Spanish
    • Birkhoff, G., Three observations on linear algebra. Univ.Nac. Tucumán. Revista A. 5 (1946), 147-151 (in Spanish).
    • (1946) Univ.Nac.Tucumán. Revista A. , vol.5 , pp. 147-151
    • Birkhoff, G.1
  • 4
    • 0003257405 scopus 로고    scopus 로고
    • Modern graph theory
    • Springer-Verlag, New York
    • Bollobás, B., Modern graph theory. Grad. Texts in Math. 184, Springer-Verlag, New York 1998.
    • (1998) Grad. Texts in Math. , vol.184
    • Bollobás, B.1
  • 5
    • 51249170707 scopus 로고
    • List-colorings of graphs
    • Bollobás, B., and Harris, A. J., List-colorings of graphs. Graphs Combin. 1 (1985), 115-127.
    • (1985) Graphs Combin. , vol.1 , pp. 115-127
    • Bollobás, B.1    Harris, A.J.2
  • 6
    • 0003269285 scopus 로고
    • Matrices of sign-solvable linear systems
    • Cambridge University Press, Cambridge
    • Brualdi, R. A., and Shader, B. L., Matrices of sign-solvable linear systems. Cambridge Tracts in Math. 116, Cambridge University Press, Cambridge 1995.
    • (1995) Cambridge Tracts in Math. , vol.116
    • Brualdi, R.A.1    Shader, B.L.2
  • 7
    • 0036266832 scopus 로고    scopus 로고
    • On a conjecture of Lovász concerning bricks. II. Bricks of finite characteristic
    • de Carvalho, M. H., Lucchesi, C. L., and Murty, U. S. R., On a conjecture of Lovász concerning bricks. II. Bricks of finite characteristic. J. Combin. Theory B 85 (2002), 137-180.
    • (2002) J. Combin. Theory B , vol.85 , pp. 137-180
    • De Carvalho, M.H.1    Lucchesi, C.L.2    Murty, U.S.R.3
  • 8
    • 16244369390 scopus 로고    scopus 로고
    • On the number of dissimilar Pfaffian orientations of graphs
    • de Carvalho, M. H., Lucchesi, C. L., and Murty, U. S. R., On the number of dissimilar Pfaffian orientations of graphs. Theor. Inform. Appl. 39 (2005), 93-113.
    • (2005) Theor. Inform. Appl. , vol.39 , pp. 93-113
    • De Carvalho, M.H.1    Lucchesi, C.L.2    Murty, U.S.R.3
  • 10
    • 33750077026 scopus 로고    scopus 로고
    • Graph theory
    • Springer-Verlag, Berlin
    • Diestel, R., Graph Theory. Grad. Texts in Math. 173, Springer-Verlag, Berlin 2005.
    • (2005) Grad. Texts in Math. , vol.173
    • Diestel, R.1
  • 12
    • 0001214263 scopus 로고
    • Maximum matching and a polyhedron with (0, 1) vertices
    • Edmonds, J., Maximum matching and a polyhedron with (0, 1) vertices. J. Res. Nat. Standards B 69 (1965), 125-130.
    • (1965) J. Res. Nat. Standards B , vol.69 , pp. 125-130
    • Edmonds, J.1
  • 13
    • 51249181400 scopus 로고
    • Brick decompositions and matching rank of graphs
    • Edmonds, J., Lovász, L., and Pulleyblank, W. R., Brick decompositions and matching rank of graphs. Combinatorica 2 (1982), 247-274.
    • (1982) Combinatorica , vol.2 , pp. 247-274
    • Edmonds, J.1    Lovász, L.2    Pulleyblank, W.R.3
  • 14
    • 0041350909 scopus 로고    scopus 로고
    • List edge colourings of some 1-factorable multigraphs
    • Ellingham, M., and Goddyn, L., List edge colourings of some 1-factorable multigraphs. Combinatorica 16 (1996), 343-352.
    • (1996) Combinatorica , vol.16 , pp. 343-352
    • Ellingham, M.1    Goddyn, L.2
  • 15
    • 0035402508 scopus 로고    scopus 로고
    • A characterisation of Pfaffian near bipartite graphs
    • Fischer, I., and Little, C., A characterisation of Pfaffian near bipartite graphs. J. Combin. Theory Ser. B 82 (2001), 175-222.
    • (2001) J. Combin. Theory Ser. B , vol.82 , pp. 175-222
    • Fischer, I.1    Little, C.2
  • 16
    • 0001566238 scopus 로고    scopus 로고
    • Statistical mechanics of dimers on a plane lattice
    • Fisher, M. E., Statistical mechanics of dimers on a plane lattice. Phys. Rev. 124, 1664-1672.
    • Phys. Rev. , vol.124 , pp. 1664-1672
    • Fisher, M.E.1
  • 17
    • 0042463264 scopus 로고    scopus 로고
    • On the theory of Pfaffian orientations I. Perfect matchings and permanents
    • Galluccio, A., and Loebl, M., On the theory of Pfaffian orientations I. Perfect matchings and permanents. Electron. J. Combin. 6 (1999).
    • (1999) Electron. J. Combin. , vol.6
    • Galluccio, A.1    Loebl, M.2
  • 18
    • 84878035311 scopus 로고    scopus 로고
    • private communication
    • Goddyn, L., private communication.
    • Goddyn, L.1
  • 19
    • 0006362327 scopus 로고
    • Geometric algorithms and combinatorial optimization
    • Springer-Verlag, Berlin
    • Grötschel, M., Lovász, L., and Schrijver, A., Geometric algorithms and combinatorial optimization. Algorithms Combin. 2, Springer-Verlag, Berlin 1993.
    • (1993) Algorithms Combin. , vol.2
    • Grötschel, M.1    Lovász, L.2    Schrijver, A.3
  • 20
    • 0000795148 scopus 로고
    • Über wesentlich unplättbare Kurven im dreidimensionalen Raume
    • Hanani, H. (Chaim Chojnacki), Über wesentlich unplättbare Kurven im dreidimensionalen Raume. Fund. Math. 23 (1934), 135-142.
    • (1934) Fund. Math. , vol.23 , pp. 135-142
    • Hanani, H.1
  • 21
    • 0000113399 scopus 로고
    • The statistics of dimers on a lattice. I. The number of dimer arrangements on a quadratic lattice
    • Kasteleyn, P.W., The statistics of dimers on a lattice. I. The number of dimer arrangements on a quadratic lattice. Physica 27 (1961), 1209-1225.
    • (1961) Physica , vol.27 , pp. 1209-1225
    • Kasteleyn, P.W.1
  • 22
    • 0001163746 scopus 로고
    • Dimer statistics and phase transitions
    • Kasteleyn, P.W., Dimer statistics and phase transitions. J. Math. Phys. 4 (1963), 287-293.
    • (1963) J. Math. Phys. , vol.4 , pp. 287-293
    • Kasteleyn, P.W.1
  • 23
    • 0001834352 scopus 로고
    • Graph theory and crystal physics
    • (ed. by F. Harary), Academic Press, New York
    • Kasteleyn, P. W., Graph theory and crystal physics. In Graph Theory and Theoretical Physics (ed. by F. Harary), Academic Press, New York 1967, 43-110.
    • (1967) Graph Theory and Theoretical Physics , pp. 43-110
    • Kasteleyn, P.W.1
  • 25
    • 84974001467 scopus 로고
    • Fluxes Laplacians and Kasteleyn's theorem
    • Lieb, E. H., and Loss, M., Fluxes, Laplacians, and Kasteleyn's theorem. Duke Math. J. 71 (1993), 337-363.
    • (1993) Duke Math. J. , vol.71 , pp. 337-363
    • Lieb, E.H.1    Loss, M.2
  • 26
    • 0007128424 scopus 로고
    • Kasteleyn's theorem and arbitrary graphs
    • Little, C. H. C., Kasteleyn's theorem and arbitrary graphs. Canad. J. Math. 25 (1973), 758-764.
    • (1973) Canad. J. Math. , vol.25 , pp. 758-764
    • Little, C.H.C.1
  • 27
    • 0000849965 scopus 로고
    • A characterization of convertible (0, 1)-matrices
    • Little, C. H. C., A characterization of convertible (0, 1)-matrices. J. Combin. Theory Ser. B 18 (1975), 187-208.
    • (1975) J. Combin. Theory Ser. B , vol.18 , pp. 187-208
    • Little, C.H.C.1
  • 28
    • 0002143066 scopus 로고
    • On chromatic number of finite set-systems
    • Lovász, L., On chromatic number of finite set-systems. Acta Math. Acad. Sci. Hungar. 19 (1968), 59-67.
    • (1968) Acta Math. Acad. Sci. Hungar. , vol.19 , pp. 59-67
    • Lovász, L.1
  • 29
    • 0000858907 scopus 로고
    • Ear-decompositions of matching covered graphs
    • Lovász, L., Ear-decompositions of matching covered graphs. Combinatorica 2 (1983), 395-407.
    • (1983) Combinatorica , vol.2 , pp. 395-407
    • Lovász, L.1
  • 30
    • 84878049304 scopus 로고
    • Some algorithmic problems on lattices
    • (ed. by L. Lovász and E. Szemerédi), Colloq. Math. Soc. Janos Bolyai 44, János Bolyai Mathematical Society, Budapest
    • Lovász, L., Some algorithmic problems on lattices. In Theory of Algorithms (ed. by L. Lovász and E. Szemerédi), Colloq. Math. Soc. Janos Bolyai 44, János Bolyai Mathematical Society, Budapest 1985, 323-337.
    • (1985) Theory of Algorithms , pp. 323-337
    • Lovász, L.1
  • 31
    • 0001347227 scopus 로고
    • Matching structure and the matching lattice
    • Lovász, L., Matching structure and the matching lattice. J. Combin. Theory Ser. B 43 (1987), 187-222.
    • (1987) J. Combin. Theory Ser. B , vol.43 , pp. 187-222
    • Lovász, L.1
  • 32
    • 0003323270 scopus 로고
    • Matching theory
    • Ann. of Discrete Math. 29, North-Holland, Amsterdam
    • Lovász, L., and Plummer, M., Matching theory. North-Holland Math. Stud. 121, Ann. of Discrete Math. 29, North-Holland, Amsterdam 1986.
    • (1986) North-Holland Math. Stud. , vol.121
    • Lovász, L.1    Plummer, M.2
  • 33
    • 23044518570 scopus 로고    scopus 로고
    • Even dicycles
    • McCuaig, W., Even dicycles. J. Graph Theory 35 (2000), 46-68.
    • (2000) J. Graph Theory , vol.35 , pp. 46-68
    • McCuaig, W.1
  • 34
    • 31244432111 scopus 로고    scopus 로고
    • Brace generation
    • McCuaig, W., Brace generation. J. Graph Theory 38 (2001), 124-169.
    • (2001) J. Graph Theory , vol.38 , pp. 124-169
    • McCuaig, W.1
  • 35
    • 9744219583 scopus 로고    scopus 로고
    • Pólya's permanent problem
    • McCuaig, W., Pólya's permanent problem. Electron. J. Combin. 11 (2004), 83pp.
    • (2004) Electron. J. Combin. , vol.11
    • McCuaig, W.1
  • 46
    • 0002099583 scopus 로고
    • Applications of negative-dimensional tensors
    • (ed. by D. J. A.Welsh), Academic Press, London
    • Penrose, R., Applications of negative-dimensional tensors. In Combinatorial Mathematics and its Applications (ed. by D. J. A.Welsh), Academic Press, London 1971, 221-244.
    • (1971) Combinatorial Mathematics and Its Applications , pp. 221-244
    • Penrose, R.1
  • 50
    • 0033235959 scopus 로고    scopus 로고
    • Permanents, Pfaffian orientations, and even directed circuits
    • Robertson, N., Seymour, P. D., and Thomas, R., Permanents, Pfaffian orientations, and even directed circuits. Math. Ann. 150 (1999), 929-975.
    • (1999) Math. Ann. , vol.150 , pp. 929-975
    • Robertson, N.1    Seymour, P.D.2    Thomas, R.3
  • 52
    • 77957183674 scopus 로고
    • On the two-colouring of hypergraphs
    • Seymour, P. D., On the two-colouring of hypergraphs. Quart. J. Math. Oxford 25 (1974), 303-312.
    • (1974) Quart. J. Math. Oxford , vol.25 , pp. 303-312
    • Seymour, P.D.1
  • 54
    • 0001700106 scopus 로고
    • Note on a theorem in geometry of position
    • Tait, P. G., Note on a theorem in geometry of position, Trans. Roy. Soc. Edinburgh 29 (1880), 657-660.
    • (1880) Trans. Roy. Soc. Edinburgh , vol.29 , pp. 657-660
    • Tait, P.G.1
  • 55
    • 84996204867 scopus 로고
    • Dimer problem in statistical mechanics-an exact result
    • Temperley, H. N. V., and Fisher, M. E., Dimer problem in statistical mechanics-an exact result. Phil. Mag. 6 (1961), 1061-1063.
    • (1961) Phil. Mag. , vol.6 , pp. 1061-1063
    • Temperley, H.N.V.1    Fisher, M.E.2
  • 56
    • 0347113873 scopus 로고    scopus 로고
    • Matching in graphs on non-orientable surfaces
    • Tesler, G., Matching in graphs on non-orientable surfaces. J. Combin. Theory Ser. B 78 (2000), 198-231.
    • (2000) J. Combin. Theory Ser. B , vol.78 , pp. 198-231
    • Tesler, G.1
  • 57
    • 84990822691 scopus 로고
    • Even cycles in directed graphs
    • Thomassen, C., Even cycles in directed graphs. European J. Combin. 6 (1985), 85-89.
    • (1985) European J. Combin. , vol.6 , pp. 85-89
    • Thomassen, C.1
  • 58
    • 0002529743 scopus 로고
    • Sign-nonsingular matrices and even cycles in directed graphs
    • Thomassen, C., Sign-nonsingular matrices and even cycles in directed graphs. Linear Algebra Appl. 75 (1986), 27-41.
    • (1986) Linear Algebra Appl. , vol.75 , pp. 27-41
    • Thomassen, C.1
  • 59
    • 84968487214 scopus 로고
    • The even cycle problem for directed graphs
    • Thomassen, C., The even cycle problem for directed graphs. J. Amer. Math. Soc. 5 (1992), 217-229.
    • (1992) J. Amer. Math. Soc. , vol.5 , pp. 217-229
    • Thomassen, C.1
  • 60
    • 38249002030 scopus 로고
    • The even cycle problem for planar digraphs
    • Thomassen, C., The even cycle problem for planar digraphs. J. Algorithms 15 (1993), 61-75.
    • (1993) J. Algorithms , vol.15 , pp. 61-75
    • Thomassen, C.1
  • 61
    • 84960567433 scopus 로고
    • The factorization of linear graphs
    • Tutte, W. T., The factorization of linear graphs. J. London Math. Soc. 22 (1947), 107-111.
    • (1947) J. London Math. Soc. , vol.22 , pp. 107-111
    • Tutte, W.T.1
  • 62
    • 0002156092 scopus 로고
    • Toward a theory of crossing numbers
    • Tutte, W. T., Toward a theory of crossing numbers, J. Combin. Theory Ser. B 8 (1971), 45-53.
    • (1971) J. Combin. Theory Ser. B , vol.8 , pp. 45-53
    • Tutte, W.T.1
  • 63
    • 49249151236 scopus 로고
    • The complexity of computing the permanent
    • Valiant, L. G., The complexity of computing the permanent. Theoret. Comput. Sci. 8 (1979), 189-201.
    • (1979) Theoret. Comput. Sci. , vol.8 , pp. 189-201
    • Valiant, L.G.1
  • 64
    • 38249006562 scopus 로고
    • Pfaffian orientations, 0-1 permanents, and even cycles in directed graphs
    • Vazirani, V.V., andYannakakis, M., Pfaffian orientations, 0-1 permanents, and even cycles in directed graphs. Discrete Appl. Math. 25 (1989), 179-190.
    • (1989) Discrete Appl. Math. , vol.25 , pp. 179-190
    • Vazirani, V.V.1    Yannakakis, M.2


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