EITHER DIGRAPHS OR PRE-TOPOLOGICAL SPACES?
Palavras-chave:
Digrafos, Espaços Pre-topologicos, Homotopia Regular para Digrafos, TorneiosResumo
Neste artigo mostramos que os digrafos podem ser identificados, de um modo natural, com espacos pre-topologicos nitos. Mostramos tambem que com esta identicação a Teoria de Homotopia Regular e a mais apropriada a ser usada quando se trabalha com digrafos. Em particular obtemos caracterizações gracas e estruturais para algumas classes de torneios, mostrando a import^ancia desta nova abordagem.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., The rst normalization theorem for regular homotopy of nite directed graphs, Rend. Ist. Mat. Univ. Trieste, 13 (1981), 38-50.
[4] BURZIO M. and DEMARIA D.C., The second and third normalization theorem for regular homotopy of nite directed graphs, Rend. Ist. Mat. Univ. Trieste, 15 (1983), 61-82.
[5] BURZIO, M. and DEMARIA, D. C., Duality theorem for regular homo-topy of nite directed graphs, Rend. Circ. Mat. Palermo, (2), 31 (1982), 371-400.
[6] BURZIO, M. and DEMARIA, D. C., Homotopy of polyhedra and regular homotopy of nite directed graphs, Atti II Conv. Topologia, Suppl. Rend. Circ. Mat. Palermo, (2), n
12 (1986), 189-204.
[7] BURZIO, M. and DEMARIA, D. C., Characterization of tournaments by coned 3-cycles, Acta Univ. Carol., Math. Phys., 28 (1987), 25-30.
[8] BURZIO, M. and DEMARIA, D. C., On simply disconnected tournaments, Proc. Catania Confer. Ars Combinatoria, 24 A (1988), 149-161.
[9] BURZIO, M. and DEMARIA, D. C., On a classication of hamiltonian tournaments, Acta Univ. Carol., Math. Phys., 29 (1988), 3-14.
[10] BURZIO, M. and DEMARIA, D. C., Hamiltonian tournaments with the least number of 3-cycles, J. Graph Theory 14 (6) (1990), 663-672.
[11] CAMION P., Quelques porpriete des chemins et circuits Hamiltoniens dans la theorie des graphes, Cahiers Centre Etudes Rech. Oper., vol 2 (1960), 5-36.
[12] CECH E.,Topological Spaces, Interscience, London (1966).
[13] DEMARIA D. C. and GARBACCIO BOGIN R.,Homotopy and ho-mology in pretopological spaces, Proc. 11 th Winter School, Suppl. Rend. Circ. Mat. Palermo, (2), N 3 (1984), 119-126.
[14] DEMARIA D.C. and GIANELLA G.M., On normal tournaments , Conf. Semin. Matem. Univ. Bari ,vol. 232 (1989), 1-29.
[15] DEMARIA D.C. and GUIDO C., On the reconstruction of normal tournaments, J. Comb. Inf. and Sys. Sci., vol. 15 (1990), 301-323.
[16] DEMARIA D.C. and KIIHL J.C. S., On the complete digraphs which are simply disconnected, Publicacions Mathematiques, vol. 35 (1991), 517-525.
[17] 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.
[18] 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.
[19] DOUGLAS R.J., Tournaments that admit exactly one Hamiltonian circuit, Proc. London Math. Soc., 21, (1970), 716-730.
[20] GUIDO C., Structure and reconstruction of Moon tournaments, J. Comb. Inf. and Sys. Sci., vol. 19 (1994), 47-61.
[21] GUIDO C., A larger class of reconstructable tournaments, Dicrete Math. 152 (1996), 171-184.
[22] GUIDO C. and KIIHL J.C.S, Some remarks on non-reconstructable tournaments, (to appear).
[23] HILTON P.J. and WYLIE S., Homology Theory, Cambridge Univ. PresS, Cambridge (1960).
[24] KOWALSKY H.J., Topological Spaces, Academic Press, New York and London (1965).
[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., NESET RIL J. and PELANT J., Either tournaments or algebras?, Discrete Math., 11 (1975), 37-66.
[29] 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).
[30] STOCKMEYER P.K., The falsity of the reconstruction conjecture for tournaments, J. Graph Theory 1 (1977), 19-25.
[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., The rst normalization theorem for regular homotopy of nite directed graphs, Rend. Ist. Mat. Univ. Trieste, 13 (1981), 38-50.
[4] BURZIO M. and DEMARIA D.C., The second and third normalization theorem for regular homotopy of nite directed graphs, Rend. Ist. Mat. Univ. Trieste, 15 (1983), 61-82.
[5] BURZIO, M. and DEMARIA, D. C., Duality theorem for regular homo-topy of nite directed graphs, Rend. Circ. Mat. Palermo, (2), 31 (1982), 371-400.
[6] BURZIO, M. and DEMARIA, D. C., Homotopy of polyhedra and regular homotopy of nite directed graphs, Atti II Conv. Topologia, Suppl. Rend. Circ. Mat. Palermo, (2), n
12 (1986), 189-204.
[7] BURZIO, M. and DEMARIA, D. C., Characterization of tournaments by coned 3-cycles, Acta Univ. Carol., Math. Phys., 28 (1987), 25-30.
[8] BURZIO, M. and DEMARIA, D. C., On simply disconnected tournaments, Proc. Catania Confer. Ars Combinatoria, 24 A (1988), 149-161.
[9] BURZIO, M. and DEMARIA, D. C., On a classication of hamiltonian tournaments, Acta Univ. Carol., Math. Phys., 29 (1988), 3-14.
[10] BURZIO, M. and DEMARIA, D. C., Hamiltonian tournaments with the least number of 3-cycles, J. Graph Theory 14 (6) (1990), 663-672.
[11] CAMION P., Quelques porpriete des chemins et circuits Hamiltoniens dans la theorie des graphes, Cahiers Centre Etudes Rech. Oper., vol 2 (1960), 5-36.
[12] CECH E.,Topological Spaces, Interscience, London (1966).
[13] DEMARIA D. C. and GARBACCIO BOGIN R.,Homotopy and ho-mology in pretopological spaces, Proc. 11 th Winter School, Suppl. Rend. Circ. Mat. Palermo, (2), N 3 (1984), 119-126.
[14] DEMARIA D.C. and GIANELLA G.M., On normal tournaments , Conf. Semin. Matem. Univ. Bari ,vol. 232 (1989), 1-29.
[15] DEMARIA D.C. and GUIDO C., On the reconstruction of normal tournaments, J. Comb. Inf. and Sys. Sci., vol. 15 (1990), 301-323.
[16] DEMARIA D.C. and KIIHL J.C. S., On the complete digraphs which are simply disconnected, Publicacions Mathematiques, vol. 35 (1991), 517-525.
[17] 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.
[18] 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.
[19] DOUGLAS R.J., Tournaments that admit exactly one Hamiltonian circuit, Proc. London Math. Soc., 21, (1970), 716-730.
[20] GUIDO C., Structure and reconstruction of Moon tournaments, J. Comb. Inf. and Sys. Sci., vol. 19 (1994), 47-61.
[21] GUIDO C., A larger class of reconstructable tournaments, Dicrete Math. 152 (1996), 171-184.
[22] GUIDO C. and KIIHL J.C.S, Some remarks on non-reconstructable tournaments, (to appear).
[23] HILTON P.J. and WYLIE S., Homology Theory, Cambridge Univ. PresS, Cambridge (1960).
[24] KOWALSKY H.J., Topological Spaces, Academic Press, New York and London (1965).
[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., NESET RIL J. and PELANT J., Either tournaments or algebras?, Discrete Math., 11 (1975), 37-66.
[29] 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).
[30] STOCKMEYER P.K., The falsity of the reconstruction conjecture for tournaments, J. Graph Theory 1 (1977), 19-25.
