Geodesic
Maximum genus, connectivity, and Nebeský's Theorem
Ars Mathematica Contemporanea, Tome 9 (2015) no. 1, pp. 51-61.

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We prove lower bounds on the maximum genus of a graph in terms of its connectivity and Betti number (cycle rank). These bounds are tight for all possible values of edge-connectivity and vertex-connectivity and for both simple and non-simple graphs. The use of Nebeský's characterization of maximum genus gives us both shorter proofs and a description of extremal graphs. An additional application of our method shows that the maximum genus is almost additive over the edge cuts.
DOI : 10.26493/1855-3974.356.66e
Keywords: Maximum genus, Nebesky theorem, Betti number, cycle rank, connectivity 
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Dan Archdeacon; Michal Kotrbčík; Roman Nedela; Martin Škoviera. Maximum genus, connectivity, and Nebeský's Theorem. Ars Mathematica Contemporanea, Tome 9 (2015) no. 1, pp. 51-61. doi : 10.26493/1855-3974.356.66e. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.356.66e/

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