×

A new characterization of the maximum genus of a graph. (English) Zbl 0482.05034


MSC:

05C10 Planar graphs; geometric and topological aspects of graph theory
PDFBibTeX XMLCite
Full Text: EuDML

References:

[1] I. Anderson: Perfect matchings of a graph. J. Combinatorial Theory 10 B (1971), 183-186. · Zbl 0172.48904 · doi:10.1016/0095-8956(71)90041-4
[2] M. Behzad G. Chartrand, L. Lesniak-Foster: Graphs & Digraphs. Prindle, Weber & Schmidt, Boston 1979. · Zbl 0403.05027
[3] R. A. Duke: The genus, regional number, and Betti number of a graph. Canad. J. Math. 18 (1966), 817-822. · Zbl 0141.21302 · doi:10.4153/CJM-1966-081-6
[4] J. Edmonds, D. R. Fulkerson: Transversals and matroid partition. J. Res. Nat. Bur. Stand. B 69 (1965), 147-153. · Zbl 0141.21801 · doi:10.6028/jres.069B.016
[5] F. Harary: Graph Theory. Addison-Wesley, Reading (Mass.) 1969. · Zbl 0196.27202
[6] N. P. Homenko: Method of \(\fi\)-transformations and some its applications. (in Ukrainian, English summary). \(\fi\)-peretvorennya grafiv (N. P. Homenko. IM AN URSR, Kiev 1973, pp. 35-96.
[7] N. P. Homenko N. A. Ostroverkhy, V. A. Kusmenko: The maximum genus of a graph. (in Ukrainian, EngHsh summary). (\(\fi\)-peretvorennya grafiv (N. P. Homenko. IM AN URSR, Kiev 1973, pp. 180-210.
[8] M. Jungerman: A characterization of upper embeddable graphs. Trans. Amer. Math. Soc. 241 (1978), 401-406. · Zbl 0379.05025 · doi:10.2307/1998852
[9] E. A. Nordhaus R. D. Ringeisen B. M. Stewart, and A. T. White: A Kuratowski-type theorem for the maximum genus of a graph. J. Combinatorial Theory 12 B (1972), 260-267. · Zbl 0217.02301 · doi:10.1016/0095-8956(72)90040-8
[10] E. A. Nordhaus B. M. Stewart, and A. T. White: On the maximum genus of a graph. J. Combinatorial Theory 11 B (1971), 258-267. · Zbl 0217.02204 · doi:10.1016/0095-8956(71)90036-0
[11] R. D. Ringeisen: Survey of results on the maximum genus of a graph. J. Graph Theory 3 (1979), 1-13. · Zbl 0398.05029 · doi:10.1002/jgt.3190030102
[12] G. Ringel: Map Color Theorem. Springer-Verlag, Berlin 1974. · Zbl 0287.05102
[13] W. T. Tutte: On the problem of decomposing a graph into n connected factors. J. London Math. Soc. 36 (1961), 221-230. · Zbl 0096.38001 · doi:10.1112/jlms/s1-36.1.221
[14] A. T. White: Graphs of groups on surfaces. Combinatorial Surveys: Proceedings of the Sixth British Combinatorial Conference (P. J. Cameron. Academic Press, London 1977, pp. 165-197. · Zbl 0378.05028
[15] R. J. Wilson: Introduction to Graph Theory. Longman, London 1972. · Zbl 0249.05101
[16] N. H. Xuong: How to determine the maximum genus of a graph. J. Combinatorial Theory 26 B (1979), 217-225. · Zbl 0403.05035 · doi:10.1016/0095-8956(79)90058-3
[17] J. W. T. Youngs: Minimal embeddings and the genus of a graph. J. Math. Mech. 12 (1963), 303-315. · Zbl 0109.41701
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.