NON-CONED CYCLES: A NEW APPROACH TO TOURNAMENTS
Palavras-chave:
Digrafos, Torneios, Homotopia regular, Ciclos conados e não-conados, Caracterstica cclica, Variedades bandeiras complexasResumo
Neste artigo apresentamos as denições e algumas propriedades basicas dos ciclos não-conados em torneios. Damos a motivação para as denições no contexto da Teoria de Homotopia Regular. Denimos o conceito de caracterstica cclica de um torneio hamiltoniano, calculando-a para algumas famlias conhecidas de torneios. Apresentamos tambem algumas aplicações onde o conceito de ciclo não-conado desempenha um papel importante, tais como teoremas de classicação, caracterizações estruturais de certas famlias de torneios e situações nas quais torneios estão associados, por exemplo, a variedades bandeiras complexas de modo a estabelecerse uma estrutura quase complexa invariante nelas admite ou não certas metricas invariantes.Referências
[1] BEINEKE, L. W. and REID, K. B., Tournaments-Selected Topics in Graph Theory, Edited by L. W. Beineke and R. J. Wilson, Academic Press, New York (1978), 169-204.
[2] BURZIO, M. and DEMARIA, D. C., A normalization theorem for regular homotopy of nite directed graphs, Rend. Circ. Matem. Palermo, (2), 30 (1981), 255-286.
[3] BURZIO, M. and DEMARIA, D. C., Duality theorem for regular homotopy of nite directed graphs, Rend. Circ. Mat. Palermo, (2), 31 (1982), 371-400.
[4] BURZIO, M. and DEMARIA, D. C., Homotopy of polyhedra and regular homotopy of nite directed graphs, Atti II o Conv. Topologia, Suppl. Rend. Circ. Mat. Palermo, (2), no 12 (1986), 189-204.
[5] BURZIO, M. and DEMARIA, D. C., Characterization of tournaments by coned 3-cycles, Acta Univ. Carol., Math. Phys., 28 (1987), 25-30.
[6] BURZIO, M. and DEMARIA, D. C., On simply disconnected tournaments, Proc. Catania Confer. Ars Combinatoria, 24 A (1988), 149-161.
[7] BURZIO, M. and DEMARIA, D. C., On a classication of hamiltonian tournaments, Acta Univ. Carol., Math. Phys., 29 (1988), 3-14.
[8] BURZIO, M. and DEMARIA, D. C., Hamiltonian tournaments with the least number of 3-cycles, J. Graph Theory 14 (6) (1990), 663-672.
[9] CAMION P., Quelques porpriete des chemins et circuits Hamiltoniens dans la theorie des graphes, Cahiers Centre
Etudes Rech. Oper., vol 2 (1960), 5-36.
[10] COHEN, N.; NEGREIROS. C.J.C. and SAN MARTIN, L.A.B., (1,2)-Symplectic metrics, ag manifolds and tournaments, Bull. London Math. ////////soc. 34 (2002),641-649.
[11] COHEN, N.; NEGREIROS. C.J.C. and SAN MARTIN, L.A.B., A rank-three condition for invariant (1,2)-symplectic almost Hermitian structure on ag manifolds, Bull. Braz. Math. Soc. (N.S.) 33 (2002).
[12] DEMARIA D. C. and GARBACCIO BOGIN R., Homotopy and homology in pretopological spaces, Proc. 11
th Winter School, Suppl. Rend. Circ. Mat. Palermo, (2), No 3 (1984), 119-126.
[13] DEMARIA D.C. and GIANELLA G.M., On normal tournaments, Conf. Semin. Matem. Univ. Bari ,vol. 232 (1989), 1-29.
[14] DEMARIA D.C. and GUIDO C., On the reconstruction of normal tournaments, J. Comb. Inf. and Sys. Sci., vol. 15 (1990), 301-323.
[15] DEMARIA D.C. and KIIHL J.C. S., On the complete digraphs which are simply disconnected, Publicacions Mathematiques, vol. 35 (1991), 517-525.
[16] DEMARIA D.C. and KIIHL J.C. S., On the simple quotients of tournaments that admit exactly one hamiltonian cycle, Atti Accad. Scienze Torino, vol. 124 (1990), 94-108.
[17] DEMARIA D.C. and KIIHL J.C. S., Some remarks on the enumeration of Douglas tournaments, Atti Accad. Scienze Torino , vol. 124 (1990), 169-185.
[18] DOUGLAS R.J., Tournaments that admit exactly one Hamiltonian circuit, Proc. London Math. Soc., 21, (1970), 716-730.
[19] GUIDO C., Structure and reconstruction of Moon tournaments, J. Comb. Inf. and Sys. Sci., vol. 19 (1994), 47-61.
[20] GUIDO C., A larger class of reconstructable tournaments, J. Comb. Inf. and Sys. Sci. (to appear).
[21] GUIDO C. and KIIHL J.C.S, Some remarks on non-reconstructable tournaments, (to appear).
[22] HILTON P.J. and WYLIE S., Homology Theory, Cambridge Univ. PresS, Cambridge (1960).
[23] MO, X. and NEGREIROS, C.J.C., Tournaments and geometry of full flag manifolds, Proc. XI Brasilian Topology Meeting (World Scientic, 2000).
[24] MO, X. and NEGREIROS, C.J.C., (1,2)-Symplectic structures on agmanifolds, Thoku Math. J. 52 (2000), 271-282.
[25] MOON J.W., Topics on Tournaments, Holt, Rinehart and Winston, New York (1978).
[26] MOON J.W., On subtournaments of a tournament, Canad. Math. Bull., vol. 9 (3) (1966), 297{301.
[27] MOON J.W., Tournaments whose subtournaments are irreducible or transitive, Canad. Math. Bull., vol. 21 (1) (1979), 75-79.
[28] MULLER, V., NESETRIL J. and PELANT J., Either tournaments or algebras?, Discrete Math., 11 (1975), 37-66.
[29] SAN MARTIN, L.A.B. and NEGREIROS. C.J.C., Invariant almost Hermitian structures on ag manifolds, Adv. Math. 178 (2003), 277-310
[30] STOCKMEYER P.K., The reconstruction conjecture for tournaments, in \Proceedings, Sixth Southeastern Conference on Combinatorics, Graph Theory and Computing" (F.Homan et al., Eds.), 561-566, Utilitas Mathematica, Winnipeg, (1975).
[31] STOCKMEYER P.K., The falsity of the reconstruction conjecture for tournaments, J. Graph Theory 1 (1977), 1925.
[2] BURZIO, M. and DEMARIA, D. C., A normalization theorem for regular homotopy of nite directed graphs, Rend. Circ. Matem. Palermo, (2), 30 (1981), 255-286.
[3] BURZIO, M. and DEMARIA, D. C., Duality theorem for regular homotopy of nite directed graphs, Rend. Circ. Mat. Palermo, (2), 31 (1982), 371-400.
[4] BURZIO, M. and DEMARIA, D. C., Homotopy of polyhedra and regular homotopy of nite directed graphs, Atti II o Conv. Topologia, Suppl. Rend. Circ. Mat. Palermo, (2), no 12 (1986), 189-204.
[5] BURZIO, M. and DEMARIA, D. C., Characterization of tournaments by coned 3-cycles, Acta Univ. Carol., Math. Phys., 28 (1987), 25-30.
[6] BURZIO, M. and DEMARIA, D. C., On simply disconnected tournaments, Proc. Catania Confer. Ars Combinatoria, 24 A (1988), 149-161.
[7] BURZIO, M. and DEMARIA, D. C., On a classication of hamiltonian tournaments, Acta Univ. Carol., Math. Phys., 29 (1988), 3-14.
[8] BURZIO, M. and DEMARIA, D. C., Hamiltonian tournaments with the least number of 3-cycles, J. Graph Theory 14 (6) (1990), 663-672.
[9] CAMION P., Quelques porpriete des chemins et circuits Hamiltoniens dans la theorie des graphes, Cahiers Centre
Etudes Rech. Oper., vol 2 (1960), 5-36.
[10] COHEN, N.; NEGREIROS. C.J.C. and SAN MARTIN, L.A.B., (1,2)-Symplectic metrics, ag manifolds and tournaments, Bull. London Math. ////////soc. 34 (2002),641-649.
[11] COHEN, N.; NEGREIROS. C.J.C. and SAN MARTIN, L.A.B., A rank-three condition for invariant (1,2)-symplectic almost Hermitian structure on ag manifolds, Bull. Braz. Math. Soc. (N.S.) 33 (2002).
[12] DEMARIA D. C. and GARBACCIO BOGIN R., Homotopy and homology in pretopological spaces, Proc. 11
th Winter School, Suppl. Rend. Circ. Mat. Palermo, (2), No 3 (1984), 119-126.
[13] DEMARIA D.C. and GIANELLA G.M., On normal tournaments, Conf. Semin. Matem. Univ. Bari ,vol. 232 (1989), 1-29.
[14] DEMARIA D.C. and GUIDO C., On the reconstruction of normal tournaments, J. Comb. Inf. and Sys. Sci., vol. 15 (1990), 301-323.
[15] DEMARIA D.C. and KIIHL J.C. S., On the complete digraphs which are simply disconnected, Publicacions Mathematiques, vol. 35 (1991), 517-525.
[16] DEMARIA D.C. and KIIHL J.C. S., On the simple quotients of tournaments that admit exactly one hamiltonian cycle, Atti Accad. Scienze Torino, vol. 124 (1990), 94-108.
[17] DEMARIA D.C. and KIIHL J.C. S., Some remarks on the enumeration of Douglas tournaments, Atti Accad. Scienze Torino , vol. 124 (1990), 169-185.
[18] DOUGLAS R.J., Tournaments that admit exactly one Hamiltonian circuit, Proc. London Math. Soc., 21, (1970), 716-730.
[19] GUIDO C., Structure and reconstruction of Moon tournaments, J. Comb. Inf. and Sys. Sci., vol. 19 (1994), 47-61.
[20] GUIDO C., A larger class of reconstructable tournaments, J. Comb. Inf. and Sys. Sci. (to appear).
[21] GUIDO C. and KIIHL J.C.S, Some remarks on non-reconstructable tournaments, (to appear).
[22] HILTON P.J. and WYLIE S., Homology Theory, Cambridge Univ. PresS, Cambridge (1960).
[23] MO, X. and NEGREIROS, C.J.C., Tournaments and geometry of full flag manifolds, Proc. XI Brasilian Topology Meeting (World Scientic, 2000).
[24] MO, X. and NEGREIROS, C.J.C., (1,2)-Symplectic structures on agmanifolds, Thoku Math. J. 52 (2000), 271-282.
[25] MOON J.W., Topics on Tournaments, Holt, Rinehart and Winston, New York (1978).
[26] MOON J.W., On subtournaments of a tournament, Canad. Math. Bull., vol. 9 (3) (1966), 297{301.
[27] MOON J.W., Tournaments whose subtournaments are irreducible or transitive, Canad. Math. Bull., vol. 21 (1) (1979), 75-79.
[28] MULLER, V., NESETRIL J. and PELANT J., Either tournaments or algebras?, Discrete Math., 11 (1975), 37-66.
[29] SAN MARTIN, L.A.B. and NEGREIROS. C.J.C., Invariant almost Hermitian structures on ag manifolds, Adv. Math. 178 (2003), 277-310
[30] STOCKMEYER P.K., The reconstruction conjecture for tournaments, in \Proceedings, Sixth Southeastern Conference on Combinatorics, Graph Theory and Computing" (F.Homan et al., Eds.), 561-566, Utilitas Mathematica, Winnipeg, (1975).
[31] STOCKMEYER P.K., The falsity of the reconstruction conjecture for tournaments, J. Graph Theory 1 (1977), 1925.
