Enumerating degree sequences in digraphs and a cycle-cocycle reversing system

European Journal of Combinatorics

Volumn 28, Issue 4, 2007, Pages 1351-1366

  Gioan, Emeric ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33847611180     PISSN: 01956698     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejc.2005.11.006     Document Type: Article

References (23)

1. Bak P. How Nature Works - The science of SOC (1997), Oxford University Press, UK
2. Biggs N. Chip firing and the critical group of a graph. J. Algebraic Combin. 9 (1999) 25-45
3. Björner A., Las Vergnas M., Sturmfels B., White N., and Ziegler G. Oriented matroids. Encyclopedia of Mathematics and its Applications vol. 46 (1993), Cambridge University Press, UK 1999
4. Björner A., Lovász L., and Shor P.W. Chip firing games on graphs. European J. Combin. 12 (1991) 283-291
5. Brylawski T., and Oxley J. The Tutte polynomial and its applications. In: White N. (Ed). Matroid Applications (1992), Cambridge University Press, UK (Chapter 6)
6. Cori R., and Le Borgne I. The Sandpile model and Tutte polynomials. Adv. Appl. Math. 30 1-2 (2003) 44-52
7. Cori R., and Rossin D. On the sandpile group of dual graphs. European J. Combin. 21 4 (2000) 447-459
8. Cori R., Rossin D., and Salvy B. Polynomial Ideals for sandpiles and their Gröbner bases. Theoret. Comput. Sci. 276 1-2 (2002) 1-15
9. Dhar D. Self-organized critical state of sandpile automaton models. Phys. Rev. Lett. 64 (1990)
10. Etienne G. On the Möbius algebra geometric lattices. European J. Combin. 19 (1998) 921-933
11. Etienne G., and Las Vergnas M. External and internal elements of a matroid basis. Discrete Math. 179 (1999) 111-119
12. E. Gioan, Circuit-cocircuit reversing system in regular matroids, Ann. Combin. (in press)
13. Gioan E., and Las Vergnas M. Active bijections between spanning trees and orientations in graphs. Discrete Math. 298 (2005) 169-188
14. E. Gioan, M. Las Vergnas, The active bijection in oriented matroids, II - Decompositions of activities (submitted for publication). See also chapter 2 in: Correspondance naturelle entre bases et réorientations des matroïdes orientés, Ph.D. Dissertation, Bordeaux 1 University, France, December, 2002
15. Greene C., and Zaslavsky T. On the interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-Radon partitions and orientations of graphs. Trans. Amer. Math. Soc. 280 (1983) 97-126
16. Kook W., Reiner V., and Stanton D. Combinatorial Laplacians of matroid complexes. J. Amer. Math. Soc. 13 (1999) 129-148
17. Latapy M., and Magnien C. Coding distributive lattices with edge firing games. Inform. Process. Lett. 83 3 (2002) 125-128
18. Las Vergnas M. The Tutte polynomial of a morphism of matroids II. Activities of orientations. Progress in Graph Theory (Proc. Waterloo Silver Jubilee Conf. 1982) (1984), Academic Press Toronto, Canada 367-380
19. Merino-López C. Chip firing and Tutte polynomial. Ann. Combin. 2 (1997) 253-259
20. Minty G.J. On the axiomatic foundations of the theories of directed linear graphs, electrical networks and network-programming. J. Math. Mech. 15 (1966) 485-520
21. Stanley R.P. Acyclic orientations of graphs. Discrete Math. 5 (1973) 171-178
22. Stanley R.P. Decompositions of rational convex polytopes. Ann. Discrete Math. 6 (1980) 333-342
23. Tutte W.T. A contribution to the theory of chromatic polynomials. Canad. J. Math. 6 (1954) 80-91