Counting subgraphs a new approach to the Caccetta-Häggkvist conjecture

Discrete Mathematics - Tập 165 - Trang 71-80 - 1997
J.A. Bondy1
1Université Claude-Bernard Lyon 1, 43 Bd du 11 Novembre 1918, 69622 Villeurbanne Cedex, France

Tài liệu tham khảo

Behzad, 1970, On minimal regular digraphs with given girth, Fund. Math., 69, 227, 10.4064/fm-69-3-227-231 Bollobás, 1978 J.A. Bondy, Counting techniques in graph theory, in preparation. Caccetta, 1978, On minimal digraphs with given girth, 21, 181 Chvátal, 1983, Short cycles in directed graphs, J. Combin. Theory Ser. B, 35, 323, 10.1016/0095-8956(83)90059-X Giraud, 1976, Sur les proportions respectives de triangles uni, bi ou tricolores dans un tricoloriage des arêtes du n-emble, Discrete Math., 16, 13, 10.1016/0012-365X(76)90090-X Giraud, 1979, Sur le problème de Goodman pour les quadrangles et la majoration des nombres de Ramsey, J. Combin. Theory Ser. B, 27, 237, 10.1016/0095-8956(79)90016-9 Goodman, 1959, On sets of acquaintances and strangers at any party, Amer. Math. Monthly, 66, 778, 10.2307/2310464 Goodman, 1985, Triangles in a complete chromatic graph with three colors, Discrete Math., 57, 225, 10.1016/0012-365X(85)90175-X de Graaf, 1992, Directed triangles in directed graphs, Discrete Math., 110, 279, 10.1016/0012-365X(92)90719-V Hamidoune, 1987, A note on minimal directed graphs with given girth, J. Combin. Theory Ser. B, 43, 343, 10.1016/0095-8956(87)90009-8 Hoàng, 1987, A note on short cycles in digraphs, Discrete Math., 66, 103, 10.1016/0012-365X(87)90122-1 Li, 1933, On minimal regular digraphs with girth 4, Czechoslovak Math. J., 33, 439, 10.21136/CMJ.1983.101894 Lovász, 1976, On the number of complete subgraphs of a graph, 431 Lovász, 1983, On the number of complete subgraphs of a graph. II, 459 Mantel, 1907, Problem 28, Wiskundige Opgaven, 10, 60 Nishimura, 1988, Short cycles in digraphs, Discrete Math., 72, 295, 10.1016/0012-365X(88)90219-1 A. Schrijver, personal communication, 1995. P.D. Seymour, personal communication, 1995. Turán, 1941, On an extremal problem in graph theory, Mat. Fiz. Lapok., 48, 436 Wong, 1982, Cages — a survey, J. Graph Theory, 6, 1, 10.1002/jgt.3190060103