【摘 要】
：
Let G be a graph with degree sequence (dv). If the maximum degree of any subgraph induced by a neighborhood of G is at most m, then the independence number of G
【机 构】
：
Department of Mathematics,Department of Mathematical Sciences
【基金项目】
：
江苏省333新世纪科学技术带头人培养工程;Science Foundation of the Education Ministry of China;国家自然科学基金
论文部分内容阅读
Let G be a graph with degree sequence (dv). If the maximum degree of any subgraph induced by a neighborhood of G is at most m, then the independence number of G is at least ∑vfm+1(dv), where fm+1(x) is a function greater than (log(x/(m+1))-1)/(x) for x>0. For a weighted graph G=(V,E,w), we prove that its weighted independence number (the maximum sum of the weights of an independent set in G) is at least ∑v(wv)/(1+dv), where wv is the weight of v.
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