Geodesic
Flows on hypermaps
Glasgow mathematical journal, Tome 30 (1988) no. 1, pp. 17-29

Voir la notice de l'article provenant de la source Cambridge University Press

The combinatorial investigation of graphs embedded on surfaces leads one to consider a pair of permutations (σ, α) that generate a transitive group [7]. The permutation α is a fixed-point-free involution and the pair is called a map. When this condition on α is dropped the combinatorial object that arises is called a hypermap. Both maps and hypermaps have a topological description: for maps a classical reference is [13] and for hypermaps such a description can be found in [4] and [6]; a brief account of it will be given below. However, the relationship between maps and hypermaps is not simply that the latter generalize the former. Actually, with every hypermap there is associated a map, its bipartite map, and conversely every bipartite map arises in this way. We do not enter into the details of this question; we refer the reader to the work of Walsh [16]. In this sense hypermaps are, at the same time, a generalization and a special case of maps. 
Cori, R.; Machi', A. Flows on hypermaps. Glasgow mathematical journal, Tome 30 (1988) no. 1, pp. 17-29. doi: 10.1017/S0017089500006996
@article{10_1017_S0017089500006996,
     author = {Cori, R. and Machi', A.},
     title = {Flows on hypermaps},
     journal = {Glasgow mathematical journal},
     pages = {17--29},
     year = {1988},
     volume = {30},
     number = {1},
     doi = {10.1017/S0017089500006996},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500006996/}
}
TY  - JOUR
AU  - Cori, R.
AU  - Machi', A.
TI  - Flows on hypermaps
JO  - Glasgow mathematical journal
PY  - 1988
SP  - 17
EP  - 29
VL  - 30
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500006996/
DO  - 10.1017/S0017089500006996
ID  - 10_1017_S0017089500006996
ER  - 
%0 Journal Article
%A Cori, R.
%A Machi', A.
%T Flows on hypermaps
%J Glasgow mathematical journal
%D 1988
%P 17-29
%V 30
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500006996/
%R 10.1017/S0017089500006996
%F 10_1017_S0017089500006996

[1] 1.Biggs, N., Algebraic graph theory (Cambridge University Press, 1974). Google Scholar | DOI

[2] 2.Brahana, H. R., Systems of circuits on two-dimensional manifolds, Ann. of Math. 23 (1921–1922), 144–168. Google Scholar | DOI

[3] 3.Cohn, M. and Lempel, A., Cycle decomposition by disjoint permutations, J. Combinatorial Theory Ser. A 13 (1972), 83–89. Google Scholar | DOI

[4] 4.Cori, R., Un code pour les graphes planaires et ses applications, Astérisque No. 27 (Societé Mathematique de France, 1975). Google Scholar

[5] 5.Cori, R. and Machi, A., Su alcune proprieta del genere di una coppia di permutazioni, Boll. Un. Mat. Ital. (5) 18A (1981), 84–89. Google Scholar

[6] 6.Cori, R., Machì, A., Penaud, J. G. and Vauquelin, B., On the automorphism group of a planar hypermap, European J. Combin. 2 (1981), 331–334. Google Scholar | DOI

[7] 7.Edmonds, J., A Combinatorial representation for polyhedral surfaces, Notices Amer. Math. Soc. 7, (1960), 646. Google Scholar

[8] 8.Jacques, A., Sur le genre d'une paire de substitutions, C. R. Acad. Sci. Paris 267 (1968), 625–627. Google Scholar

[9] 9.Jacques, A., Constellations et graphes topologiques, Combinatorial Theory and its applications, Colloq. Math. Soc. Janos Bolyai (1970), 657–673. Google Scholar

[10] 10.Jaeger, F., On some algebraic properties of graphs, Progress in graph theory (Waterloo, Oct. 1982) 347–366 (Academic Press, Toronto 1984). Google Scholar

[11] 11.Jones, G. A. and Singerman, D., Theory of maps on orientable surfaces, Proc. London Math. Soc. (3) 37 (1978), 273–307. Google Scholar | DOI

[12] 12.Machi, A., The Riemann Hurwitz formula for the centralizer of a pair of permutations, Archiv der Math. 42 (1984), 280–288. Google Scholar | DOI

[13] 13.Ringel, G., Map colour theorem, (Springer Verlag 1974). Google Scholar | DOI

[14] 14.Stahl, S., On the product of certain permutations, to appear. Google Scholar

[15] 15.Tutte, W. T., Graph Theory, Encyclopedia of Mathematics and its Applications, 21 (Addison-Wesley, 1984). Google Scholar

[16] 16.Walsh, T. R. S., Hypermaps versus bipartite maps, J. Combinatorial Theory Ser. B 18 (1975), 155–163. Google Scholar | DOI

Cité par Sources :