科研之友
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摘要
An edge-weighting vertex colouring of a graph is an edge-weight assignment such that the accumulated weights at the vertices yield a proper vertex colouring. If such an assignment from a set S exists, we say the graph is S-weight colourable.
We consider the S-weight colourability of digraphs by defining the accumulated weight at a vertex to be the sum of the inbound weights minus the sum of the outbound weights. Bartnicki etal. showed that every digraph is S-weight colourable for any set S of size 2 and asked whether one could show the same result using an algebraic approach. Using the Combinatorial Nullstellensatz and a classical theorem of Schur, we provide such a solution.
- 出版日期2011-1-19
