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A Kotzig type theorem for non-orientable surfaces. (English) Zbl 1141.05028
The weight of an edge in a graph $$G$$ is the sum of the degrees of its end vertices. The weight of $$G$$, $$w(G)$$, is the minimum weight among all its edges. The authors show that for a graph with minimum degree at least 3 which is embeddable in a non-orientable surface of genus $$q \geq 1$$ the following holds: $$w(G)\leq 2q+11$$ for $$1\leq q\leq 2$$, $$w(G)\leq 2q+9$$ for $$3\leq q\leq 5$$, otherwise $$w(G)\leq 2q+7$$; and the bounds are best possible.

##### MSC:
 05C10 Planar graphs; geometric and topological aspects of graph theory
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##### References:
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