The number of independent sets in graphs
The number of independent sets in graphs
复制标题
图中独立集的数量
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
A. A. Sapozhenko
中科院分区：
文献类型：
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作者：
A. A. Sapozhenko
摘要证明了以下定理：设G是一个有n个顶点的κ正则图，使得图G的独立集的最大大小等于μ。则i(G)≤
$$2^{\mu \log } (1 + \tfrac{n}{{2\mu }}) + O(n\sqrt {k^{ - 1} \log k} )$$
． 这个命题推广到拟正则图的情况。作为推论，得到了扩充器中独立集个数的上界。
AbstractThe following theorem is proved: Let G be a κ-regular graph with n vertices such that the maximal size of an independent set of the graph G is equal to μ. Then i(G) ≤
$$2^{\mu \log } (1 + \tfrac{n}{{2\mu }}) + O(n\sqrt {k^{ - 1} \log k} )$$
. This statement is generalized to the case of quasi-regular graphs. As a corollary, an upper bound for the number of independent sets in extenders is obtained.