The maximum genus of graph bundles. (English) Zbl 0642.05019

The upper embeddability of Cartesian and strong graph bundles with non- trivial base and fibre is proved. A similar result is obtained for both versions of lexicographic bundles. As a corollary the upper embeddability of Cartesian, strong and lexicographic products is obtained. The results cannot be generalized to the Cartesian and strong bundles with discrete fibres, i.e., to covering graphs. In this case sharp upper and lower bounds for Betti deficiency are obtained.


05C10 Planar graphs; geometric and topological aspects of graph theory
05C35 Extremal problems in graph theory
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