Permanents, Pfaffian orientations, and even directed circuits

Annals of Mathematics

Volumn 150, Issue 3, 1999, Pages 929-975

  Robertson, Neil ^a   Seymour, P D ^b,c   Thomas, Robin ^d  

^a OHIO STATE UNIVERSITY   (United States)

^b TELCORDIA TECHNOLOGIES   (United States)

^c PRINCETON UNIVERSITY   (United States)

^d GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033235959     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/121059     Document Type: Article

References (26)

1. R. A. BRUALDI and B. L. SHADER, Matrices of Sign-Solvable Linear Systems, Cambridge Tracts in Math. 116, Cambridge Univ. Press, Cambridge, 1995.
2. T. H. CORMEN, C. E. LEISERSON, and R. L. RIVEST, Introduction to Algorithms, McGraw-Hill, New York, 1995.
3. A. GALLUCCIO and M. LOEBL, Even cycles and H-homeomorphisms, preprint.
4. 5/2 algorithm for maximum matchings in bipartite graphs, SIAM J. Comput. 2 (1973), 225-231.
5. J. E. HOPCROFT and R. E. TARJAN, Dividing a graph into triconnected components, SIAM' J. Comput. 2 (1973), 135-158.
6. P. W. KASTELEYN, Dimer statistics and phase transitions, J. Mathematical Phys. 4 (1963), 287-293.
7. P. W. KASTELEYN, Graph theory and crystal physics, Graph Theory and Theoretical Physics (F. Harary, ed.), Academic Press, New York, 1967, 43-110.
8. V. KLEE, R. LADNER, and R. MANBER, Signsolvability revisited, Linear Algebra Appl. 59 (1984), 131-157.
9. C. H. C. LITTLE, A characterization of convertible (0, 1)-matrices, J. Combinatorial Theory 18 (1975), 187-208.
10. C. H. C. LITTLE and F. RENDL, Operations preserving the Pfaffian property of a graph, J. Austral. Math. Soc. 50 (1991), 248-257.
11. L. LOVÁSZ, On chromatic number of finite set-systems, Acta Math. Acad. Sci. Hungar. 19 (1968), 59-67.
12. _, Matching structure and the matching lattice, J. Combinatorial Theory 43 (1987), 187-222.
13. L. LOVÁSZ and M. PLUMMER, Matching Theory, Ann. of Discrete Math. 29, North-Holland, New York, 1986.
14. W. MCCUAIG, Pólya's permanent problem, preprint.
15. _, Generating braces, preprint.
16. W. MCCUAIG, N. ROBERTSON, P. D. SEYMOUR, and R. THOMAS, Permanents, Pfaffian orientations, and even directed circuits (Extended abstract), Proc. 1997 Symposium on the Theory of Computing (STOC).
17. G. PÓLYA, Aufgabe 424, Arch. Math. Phys. Ser. 20 (1913), 271.
18. P. D. SEYMOUR, On the two-colouring of hypergraphs, Quart. J. Math. Oxford 25 (1974), 303-312.
19. P. D. SEYMOUR and C. THOMASSEN, Characterization of even directed graphs, J. Combinatorial Theory 42 (1987), 36-45.
20. C. THOMASSEN, Even cycles in directed graphs, European J. Combin. 6 (1985), 85-89.
21. _, Sign-nonsingular matrices and even cycles in directed graphs, Linear Algebra and Appl. 75 (1986), 27-41; Erratum: Linear Algebra Appl. 240 (1996), 238.
22. _, The even cycle problem for directed graphs, J. A.M.S. 5 (1992), 217-229.
23. _, The even cycle problem for planar digraphs, J. Algorithms 15 (1993), 61-75.
24. L. G. VALIANT, The complexity of computing the permanent, Theoret. Comput. Sci. 8 (1979), 189-201.
25. V. V. VAZIRANI and M. YANNAKAKIS, Pfaffian orientations, 0-1 permanents, and even cycles in directed graphs, Discrete Appl. Math. 25 (1989), 179-190.
26. S. G. WILLIAMSON, Depth-first search and Kuratowski subgraphs, J. Assoc. Comput. Mach. 31 (1984), 681-693.