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Lower bounds for the average genus of a CF-graph. (English) Zbl 1204.05040

Summary: CF-graphs form a class of multigraphs that contains all simple graphs. We prove a lower bound for the average genus of a CF-graph which is a linear function of its Betti number. A lower bound for average genus in terms of the maximum genus and some structure theorems for graphs with a given average genus are also provided.

MSC:

05C10 Planar graphs; geometric and topological aspects of graph theory
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