Erdos-Sos猜想的注记
note on Erdos-Sos Conjecture
Erd"{o}s和S'{o}s在1963年提出了如下著名的猜想：若图$G$的平均度大于$k-2$,则$G$包含任一含$k$个顶点的树。Gary在2010年证明了猜想对$kleq 8$成立。本文对任一9个顶点的树$T$按照其最大度$Delta(T)$进行分类,证明了$k=9$时猜想成立,从而猜想对$kleq 9$成立。
Erd"{o}s and S'{o}s conjectured in 1963 that if the average degree of graph $G$ exceeds $k-2$,then $G$contains every tree on $k$ vertices.In 2010,Gary proved the case where $kleq 8$.We use the method of classifying the cases by $Delta(T)$,the maximum degree of tree $T$,to prove the conjecture for the case where $k=9$.Thus the conjecture is true for $kleq 9$.
张晓东、杨国斌
数学
图论Erdos-Sos猜想树最大度
Graph TheoryErdos-Sos Conjecturetreemaximum degree
张晓东,杨国斌.Erdos-Sos猜想的注记[EB/OL].(2014-03-17)[2025-08-10].http://www.paper.edu.cn/releasepaper/content/201403-509.点此复制
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