Geodesic
Non-orientable Maps and Hypermaps with Few Faces
Journal for geometry and graphics, Tome 7 (2003) no. 2, pp. 173-19 Cet article a éte moissonné depuis la source Heldermann Verlag

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A map, or a cellular division of a compact surface, is often viewed as a cellular imbedding of a connected graph in a compact surface. It generalises to a hypermap by replacing "graph" with "hypergraph". In this paper we classify the non-orientable regular maps and hypermaps with size a power of 2, the non-orientable regular maps and hypermaps with 1, 2, 3, 5 faces and give a sufficient and necessary condition for the existence of regular hypermaps with 4 faces on non-orientable surfaces. For maps we classify the non-orientable regular maps with a prime number of faces. These results can be useful in classifications of non-orientable regular hypermaps or in non-existence of regular hypermaps in some non-orientable surface.
Classification : 05C25, 05C30, 05C65, 05B45, 52C20, 57M07, 57M15, 57M50, 57M60
Mots-clés : Maps, hypermaps, graphs imbeddings, non-orientable surfaces 
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     author = {S. Wilson and A. Breda d'Azevedo},
     title = {Non-orientable {Maps} and {Hypermaps} with {Few} {Faces}},
     journal = {Journal for geometry and graphics},
     pages = {173--19},
     year = {2003},
     volume = {7},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2003_7_2_JGG_2003_7_2_a4/}
}
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S. Wilson; A. Breda d'Azevedo. Non-orientable Maps and Hypermaps with Few Faces. Journal for geometry and graphics, Tome 7 (2003) no. 2, pp. 173-19. http://geodesic.mathdoc.fr/item/JGG_2003_7_2_JGG_2003_7_2_a4/