Crossing numbers of graph embedding pairs on closed surfaces

Journal of Graph Theory

Volumn 36, Issue 1, 2001, Pages 8-23

  Negami, Seiya ^a  

^a YOKOHAMA NATIONAL UNIVERSITY   (Japan)

Author keywords

Crossing numbers; Embeddings of graphs

Indexed keywords

EID: 25444529715     PISSN: 03649024     EISSN: None     Source Type: Journal    
DOI: 10.1002/1097-0118(200101)36:1<8::AID-JGT2>3.0.CO;2-O     Document Type: Article

References (13)

1. D. Archdeacon and C. P. Bonnington, Two maps on a surface, to appear in J Graph Theory.
2. D. Barnette, Generating the triangulations of the projective plane, J Combin Theory Ser B 33 (1982), 222-230.
3. R. Brunet, A. Nakamoto, and S. Negami, Diagonal flips of triangulations on closed surfaces preserving specified properties, J Combin Theory ser B 68 (1996), 295-309.
4. Z. Gao, R. B. Richter, and P. D. Seymour, Irreducible triangulations of surfaces, J Combin Theory Ser B 68 (1996), 206-217.
5. H. Komuro, A. Nakamoto, and S. Negami, Diagonal flips in triangulations on closed surfaces with minimum degree at least 4, J Combin Theory Ser B 76 (1999), 68-92.
6. S. Lins, A minimax theorem on circuits in projective graphs, J Combin Theory Ser B 30 (1981), 253-262.
7. A. Malnic and R. Nedela, k-minimal triangulations of surfaces, Acta Math Univ Comen New Ser 64 (1995), 57-76.
8. S. Negami and S. Watanabe, Diagonal transformations of triangulations on surfaces, Tsukuba J Math 14 (1990), 155-166.
9. S. Negami and A. Nakamoto, Diagonal transformations of graphs on closed surfaces, Sci Rep Yokohama Nat Univ Sec I 40 (1993), 71-97.
10. S. Negami, Diagonal flips in triangulations on surfaces, Discrete Math 135 (1994), 225-232.
11. S. Negami, Diagonal flips of triangulations on surfaces, a survey, Yokohama Math J 47 (Special issue) (1999), 1-40.
12. N. Robertson and P. Seymour, Graph minor VII, Disjoint paths on a surface, J Combin Theory Ser B 39 (1988), 212-254.
13. N. Robertson and R. Vitray, "Representativity of surface embedding, paths, flows, and VLSI-layout," Algorithm and combinatorics, Vol. 9, B. Korte, L. Lovász, H. J. Prömel, and A. Schrijver, (Editors), Springer-Verlag, Berlin, 1990, pp. 293-328.