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On the chromatic number of the preferential attachment graph
European Journal of Combinatorics ( IF 1.0 ) Pub Date : 2021-05-29 , DOI: 10.1016/j.ejc.2021.103365 Lyuben Lichev
中文翻译:
关于优先依附图的色数
更新日期:2021-05-30
European Journal of Combinatorics ( IF 1.0 ) Pub Date : 2021-05-29 , DOI: 10.1016/j.ejc.2021.103365 Lyuben Lichev
We prove that for every and every , the chromatic number of the preferential attachment graph is asymptotically almost surely equal to . The proof relies on a combinatorial construction of a family of digraphs of chromatic number followed by a proof that asymptotically almost surely there is a digraph in this family, which is realised as a subgraph of the preferential attachment graph.
中文翻译:
关于优先依附图的色数
我们证明对于每个 并且每 , 优先附着图的色数 渐近地几乎肯定等于 . 证明依赖于色数有向图族的组合构造 随后证明渐近几乎肯定在这个族中有一个有向图,它被实现为优先连接图的一个子图。