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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.

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