| Title:
|
Characterizing the maximum genus of a connected graph (English) |
| Author:
|
Nebeský, Ladislav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
1993 |
| Pages:
|
177-185 |
| . |
| Category:
|
math |
| . |
| MSC:
|
05C10 |
| MSC:
|
05C35 |
| idZBL:
|
Zbl 0788.05033 |
| idMR:
|
MR1205240 |
| DOI:
|
10.21136/CMJ.1993.128386 |
| . |
| Date available:
|
2009-09-24T09:28:36Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128386 |
| . |
| Reference:
|
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| Reference:
|
[2] M. Behzad, G. Chartrand and L. Lesniak-Foster: Graphs & Digraphs.Prindle, Weber & Schmidt, Boston, 1979. MR 0525578 |
| Reference:
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[3] C. Berge: Théorie des graphes et ses applications.Dunod, Paris, 1958. MR 0102822 |
| Reference:
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[4] J. A. Bondy and U.S.R. Murty: Graph Theory with Applications.MacMillan, London, 1976. MR 0411988 |
| Reference:
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[5] R. A. Duke: The genus, regional number, and Betti number of a graph.Canad. J. Math 18 (1966), 817–822. Zbl 0141.21302, MR 0196731, 10.4153/CJM-1966-081-6 |
| Reference:
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[6] P. Hall: On representatives of subsets.J. London Math. Soc. 10 (1935), 26–30. Zbl 0010.34503, 10.1112/jlms/s1-10.37.26 |
| Reference:
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[7] N. P. Homenko and A. D. Glukhov: Single-component 2-cell embeddings and the maximum genus of a graph.In: Some Topological and Combinatorial Properties of Graphs, preprint 80.8, N. P. Homenko (ed.), IM AN USSR, Kiev, 1980, pp. 5–23. (Russian) MR 0583197 |
| Reference:
|
[8] N. P. Homenko, N. A. Ostroverkhy and V. A. Kusmenko: The maximum genus of a graph.In: $\varphi $-Transformations of Graphs, N. P. Homenko (ed.), IM AN URSR, Kiev, 1973, pp. 180–207. |
| Reference:
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[9] M. Jungerman: A characterization of upper-embeddable graphs.Trans. Amer. Math. Soc. 241 (1978), 401–406. Zbl 0379.05025, MR 0492309 |
| Reference:
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[10] L. Nebeský: A new characterization of the maximum genus of a graph.Czechoslovak Math. J. 31 (106) (1981), 604–613. MR 0631605 |
| Reference:
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[11] E. A. Nordhaus, B. M. Stewart and A. T. White: On the maximum genus of a graph.J. Combinatorial Theory B 11 (1971), 258–267. MR 0286713, 10.1016/0095-8956(71)90036-0 |
| Reference:
|
[12] R. Rado: A theorem on independence relations.Quart. J. Math. (Oxford) 13 (1942), 83–89. Zbl 0063.06369, MR 0008250, 10.1093/qmath/os-13.1.83 |
| Reference:
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[13] G. Ringel: The combinatorial map color theorem.J. Graph Theory 1 (1977), 141–155. Zbl 0386.05030, MR 0444509, 10.1002/jgt.3190010210 |
| Reference:
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[14] J. Širáň: Duke’s theorem does not extend to signed graph embeddings.Discrete Math. 94 (1991), 233–238. MR 1138602, 10.1016/0012-365X(91)90029-2 |
| Reference:
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[15] J. Širáň and M. Škoviera: Characterization of the maximum genus of a signed graph.J. Combinatorial Theory B 52 (1991), 124–146. MR 1109428, 10.1016/0095-8956(91)90099-6 |
| Reference:
|
[16] W. T. Tutte: The factorization of linear graphs.J. London Math. Soc. 22 (1947), 107–111. Zbl 0029.23301, MR 0023048 |
| Reference:
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[17] A. T. White: Graphs, Groups, and Surfaces.North Holland, Amsterdam, 1973. Zbl 0268.05102 |
| Reference:
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[18] R. J. Wilson: Introduction to Graph Theory.Longman Group, London, 1975. MR 0826772 |
| Reference:
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[19] N. H. Xuong: How to determine the maximum genus of a graph.J. Combinatorial Theory B 26 (1979), 217–225. Zbl 0403.05035, MR 0532589, 10.1016/0095-8956(79)90058-3 |
| . |
