科研之友
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摘要
A weighting of the edges of a hypergraph is called vertex-coloring if the weighted degrees of the vertices yield a proper coloring of the graph, i.e. every edge contains at least two vertices with different weighted degrees. In this article, we show that such a weighting is possible from the weight set {1, 2,..., max{5, r + 1}} for all hypergraphs with maximum edge size r >= 3 and not containing edges solely consisting of identical vertices. The number r + 1 is best possible for this statement.
- 出版日期2017-7
