Un code pour les graphes planaires et ses applications

Cori, Robert

Astérisque, no. 27 (1975) , 178 p.

MR Zbl | 7 citations dans Numdam

@book{AST_1975__27__1_0,
     author = {Cori, Robert},
     title = {Un code pour les graphes planaires et ses applications},
     series = {Ast\'erisque},
     year = {1975},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {27},
     mrnumber = {404045},
     zbl = {0313.05115},
     language = {fr},
     url = {https://www.numdam.org/item/AST_1975__27__1_0/}
}

TY  - BOOK
AU  - Cori, Robert
TI  - Un code pour les graphes planaires et ses applications
T3  - Astérisque
PY  - 1975
IS  - 27
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/AST_1975__27__1_0/
LA  - fr
ID  - AST_1975__27__1_0
ER  -

%0 Book
%A Cori, Robert
%T Un code pour les graphes planaires et ses applications
%S Astérisque
%D 1975
%N 27
%I Société mathématique de France
%U https://www.numdam.org/item/AST_1975__27__1_0/
%G fr
%F AST_1975__27__1_0

Cori, Robert. Un code pour les graphes planaires et ses applications. Astérisque, no. 27 (1975), 178 p. https://www.numdam.org/item/AST_1975__27__1_0/

Bibliographie
Cité par

[1] C. Berge. Théorie des graphes et ses applications. Dunod, Paris, 1963. | MR | Zbl

[2] C. Berge. Principes de Combinatoire. Dunod, Paris, 1968. | MR | Zbl

[3] C. Berge. Graphes et hypergraphes. Dunod, Paris, 1970. | MR | Zbl

[4 ] W. G. Brown. Enumeration of non separable planar maps. Can. J. Math. 15 (1963), 526-545. | MR | Zbl | DOI

[5] W. G. Brown. Enumeration of triangulations of the disk. Proc. London Math. Soc. 14 (1964), 746-768. | MR | Zbl | DOI

[6] W. G. Brown. Enumeration of quadrangular dissections of the disk. Canad. J. Math. 17 (1965), 302-317. | MR | Zbl | DOI

[7] W. G. Brown. A historical note on a recurrent combinatorial problem. Amer. Math. Monthly 72 (1965), 973-977. | MR | Zbl

[8] W. G. Brown. On the existence of square roots in certain rings of power series. Math. Annalen 158 (1965), 82-89. | MR | Zbl | EuDML | DOI

[9] W. G. Brown On the enumeration of non planar maps. Mem. Amer. Math. Soc. 65 (1966), 1-42. | MR | Zbl

[10] W. G. Brown et W. T. Tutte. On the enumeration of rooted non separable planar maps. Can. J. Math. 16 (1964), 572-577. | MR | Zbl | DOI

[11] C. Choffrut. Un code pour les triangulations. Manuscrit non publié.

[12] N. Chomsky et M. P. Schützenberger. The algebraic theory of context free languages ; in "Computer Programming and Formal Languages" (P. Braffort et D. Hirschberg, edit.) p. 118-161, North Holland, Amsterdam, (1963). | MR | Zbl | DOI

[13] R. Cori. Graphes planaires et systèmes de parenthèses. Thèse de 3ème cycle, Paris, 1969.

[14] R. Cori. Planar maps and bracketting systems in : Combinatorial structures and their applications. Gordon Breach, New-York, 1970. | Zbl

[15] R. Cori. Sur la rationalité de certaines séries génératrices. Discrete Mathematics 3 (1972), 215-31. | MR | Zbl

[16] R. Cori. Sur un opérateur lié aux graphes planaires. C.R. Acad. Sci. Paris 274 (1972), 1197-1200. | MR | Zbl

[17] R. Cori et J. Richard. Enumération des graphes planaires à l'aide des séries formelles en variables non commutatives. Discrete Mathematics 2 (1972), 115-162. | MR | Zbl

[18] G. Demoucron, Y. Malgrange, R. Pertuiset. Reconnaissance et construction de représentations planaires topologiques. Revue Française de Recherche Opérationnelle 30 (1964) 33-47. | Zbl

[19] J. Edmonds. A Combinatorial Representation for Polyhedral surfaces. Notices Amer. Math. Soc. 7 (1960) 646.

[20] S. Eilenberg. Livre à paraître.

[21] M. Fliess. Transductions algébriques. R.I.R.O. 4 (1970) R1 109-125. | DOI | MR | Zbl | EuDML | Numdam

[22] M. Fliess. Sur certaines familles de séries formelles. Thèse Sc. Math. Univ. Paris VII, Paris, 1972.

[23] D. Foata, M. P. Schützenberger. Théorie géométrique des polynômes Eulériens. Springer Verlag, Berlin, 1970, (Lecture Notes in Mathematics N° 138). | MR | Zbl

[24] S. Ginsburg. The Mathematical Theory of Context Free Languages. Mc Graw Hill, New-York, 1966. | MR | Zbl

[25] I. J. Good. Generalisations to several variables of Lagrange's expantion. Proc. Canb. Phil. Soc. 56 (1960) 367-380. | MR | Zbl | DOI

[26] M. Gross. Applications géométriques des langages formels. I.C.C. Bul., 5 (1961) 141-168.

[27] M. Gross et A. Lentin. Notions sur les grammaires formelles. Gauthier Villars, Paris, 1967. | MR | Zbl

[28] W. Gustin. Orientable embeddings of Cayley Graphs. Bull. Amer. Math. Soc. 69 (1963) 272-275. | MR | Zbl | DOI

[29] F. Harary, G. Prins et W. T. Tutte. The number of Plane Trees. Indag Math. 26 (1964) 319-329. | MR | Zbl | DOI

[30] A. Jacques. Sur le genre d'une paire de substitutions. CR. Acad. Sci. Paris 267 (1968) 625-627. | MR | Zbl

[31] A. Jacques. Constellations et propriétés algébriques des graphes topologiques. Thèse de 3ème cycle, Paris, 1969.

[32] A. Jacques. Constellations et graphes topologiques, in P. Erdös et. al. eds. Combinatorial Theory and its Applications, (Colloq. Math. Soc. Janos Bolyai.) North Holland, Amsterdam, 1970 (p.657-672). | Zbl

[33] D. A. Klarner. Correspondance between plane trees and binary sequences. J. Comb. Theory 9 (1970) 401-411. | MR | Zbl | DOI

[34] W. Kuich. Languages and the enumeration of planted plane trees. Indag. Math. 32 (1970) 268-280. | MR | Zbl

[35] J. Lederberg. "Dendral 64" : A system for computer construction, enumeration and notation of organic molecules as tree structures and cyclic graphs. Interim report National Aeronautics and Space (Administration Grant NsG 81-60, NASA CR 68 898), 1965.

[36] A. B. Lehman. A Bijective Census of Rooted Planar Maps. Communication at Ontario Math. Conf. (1970).

[37] A. Lempel, S. Even, I. Cederbaum. An Algorithm for planarity testing of Graphs, dans P. Rosenstiehl ed. Theorie des Graphes, Rome I.C.C. Dunod, 1967, 215-232. | MR | Zbl

[38] R. C. Lyndon. On Dehn's Algorithm. Math. Annalen 166 (1966) 208-228. | MR | Zbl | EuDML | DOI

[39] W. Magnus, A. Karass et D. Solitar. Combinatorial Group Theory. Interscience Publisher, J. Wiley & Sons, New-York, 1966. | MR | Zbl

[40] Mondshein. Combinatorial orderings and embedding of Graphs. Tech. Note 1971-35 Lincoln Laboratory M.I.T., 1971.

[41] R. C. Mullin. On counting rooted triangular maps. Canad. J. Math. 17 (1965) 373-382. | MR | Zbl | DOI

[42] R. C. Mullin. The enumeration of rooted triangular maps. Amer. Math. Monthly 71 (1964) 1007-1010. | MR | Zbl | DOI

[43] R. C. Mullin. The enumeration of Hamiltonian polygons in triangular maps. Pacific J. Math. 16 (1966) 139-145. | MR | Zbl | DOI

[44] R. C. Mullin. On the average number of trees in certain maps. Canad. J. Math. 17 (1965) 33-41. | MR | Zbl

[45] R. C. Mullin et P. J. Schellenberg. The enumeration of $c$ -nets via quadrangulations. J. Comb. Theory 4 (1968) 259-276. | MR | Zbl | DOI

[46] R. C. Mullin et R. G. Stanton. A map theoretic approach to Davenport Schinzel sequences. Pacific J. Maths 40 (1972) 167-172. | MR | Zbl | DOI

[47] M. Nivat. Transductions des langages de Chomsky. Ann. Inst. Fourier 18 (1968) 339-456. | DOI | MR | Zbl | EuDML | Numdam

[48] O. Ore. The four colour problem. Academic Press, New-York (1967). | MR | Zbl

[49] G. Raney. Functional composition patterns and Power series reversion. Trans. Amer. Math. Soc. 94 (1960) 441-451. | MR | Zbl | DOI

[50] J. Richard. Sur un type d'équations liées à certains problèmes combinatoires. C.R. Acad. Sci. Paris 272 (1971) 203-206. | MR | Zbl

[51] J. Richard. Sur certaines équations intervenant dans l'énumération des graphes planaires. in Logique et Automates Séminaires I.R.I.A. (1971). | Zbl

[52] P. E. Schupp. On Dehn's algorithm and the conjugacy Problem. Math. Annalen 178 (1968) 119-130. | MR | Zbl | EuDML | DOI

[53] M. P. Schützenberger. On the definition of a family of Automata. Information and Control, 4 (1961) p. 245-270. | MR | Zbl | DOI

[54] M. P. Schützenberger. On a theorem of R. Jungen. Proc. Amer. Math. Soc. 13 (1962) 885-890. | MR | Zbl | DOI

[55] M. P. Schützenberger. Le théorème de Lagrange selon N. Raney. in Logique et automates Séminaires I.R.I.A. (1971). | Zbl

[56] Serret. Cours d'Algèbre supérieure 2, 3ème ed. Gauthier Villars, Paris, 1866. | JFM

[57] Tarjan. An efficient planarity algorithm. Ph. Dissertation Stanford University (1971).

[58] W. T. Tutte. A Census of planar triangulations. Canad. J. Math. 14 (1962) 21-38. | MR | Zbl | DOI

[59] W. T. Tutte. A Census of Hamiltonian polygons. Canad. J. Math. 14 (1962) 402-417. | MR | Zbl | DOI

[60] W. T. Tutte. A Census of Slicings. Canad. J. Math. 14 (1962) 708-722. | MR | Zbl | DOI

[61] W. T. Tutte. A Census of Planar Maps. Canad. J. Math. 15 (1963) 249-271. | MR | Zbl | DOI

[62] W. T. Tutte. A New Branch of enumerative graph theory. Bull. Amer. Math. Soc. 65 (1962) 500-504. | MR | Zbl | DOI

[63] W. T. Tutte. Topics in graph theory. in Harary : Graph theory and theoretical physics Academic Press, New-York, 1967. | MR | Zbl

[64] W. T. Tutte. On the enumeration of planar maps. Bull. Amer. Math. Soc. 74 (1968) 64-74. | MR | Zbl | DOI

[65] W. T. Tutte. On the enumeration of almost bicubic rooted maps. Rand. Corp. (February 1969).

[66] W. T. Tutte. On the enumeration of four coloured maps. Siam J. Appl. Math. 17 (1969) 454-460. | MR | Zbl | DOI

[67] W. T. Tutte. On the enumeration of two coloured, rooted, and weighted Plane Trees. Equations Mathematicae 4 (1970) 143-156. | MR | Zbl | EuDML

[68] W. T. Tutte. What is a map. A paraître dans Proceeding of the Michigan Conference on Graph Theory, 1971. | Zbl

[69] Van Kampen. On some lemmas in the theory of groups. Ann. J. Math. 55 (1933) 268-273. | MR | Zbl | JFM

[70] T. Walsh. Combinatorial Enumeration of Non Planar Maps. Ph. Dissertation Toronto (1971). | MR

[71] T. Walsh, A. B. Lehman. Counting rooted maps by genus. I. J. Comb. Theory 13B (1972) 192-218. | MR | Zbl | DOI

[72] T. Walsh, A. B. Lehman. Counting rooted maps by genus. II. J. Comb. Theory 13B (1972) 122-141. | MR | Zbl | DOI

[73] C. M. Weinbaum. Visualizing the Word Problem with an application to sixthgroups. Pacific J. Math. 16 (1966) 557-578. | MR | Zbl | DOI

[74] H. Whitney et W. T. Tutte. Kempe chains and the four colour problem.Utilitas Mathematica (Winnipeg) 2 (1972) 241-281. | MR | Zbl

[75] E. T. Whittaker et G. N. Watson. A course of Modern analysis. Cambridge University Press, Cambridge, 1940. | MR