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The weight of a graph. (English) Zbl 0773.05066
Combinatorics, graphs and complexity, Proc. 4th Czech. Symp., Prachatice/Czech. 1990, Ann. Discrete Math. 51, 113-116 (1992).
[For the entire collection see Zbl 0748.00023.]
The weight of an edge in a graph $$G$$ is the sum of degrees of its end vertices. The weight of $$G$$, $$w(G)$$, is the minimum weight among all its edges. The author shows that for a graph with minimum degree at lest 3 and genus $$g$$ it holds $$w(G)\leq 2g+13$$ for $$0\leq g\leq 3$$, otherwise $$w(G)\leq 4g+7$$; and the bounds are best possible.

##### MSC:
 05C35 Extremal problems in graph theory
##### Keywords:
weight; genus; bounds
Zbl 0748.00023