| 最长路原理与图中的路和圈 |
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| 引用本文： | 高敬振. 最长路原理与图中的路和圈[J]. 山东师范大学学报(自然科学版), 1995, 0(1) |
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| 作者姓名： | 高敬振 |
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| 作者单位： | 山东师范大学数学系 |
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| 摘 要： | 设（其中）为图Ｇ中一条最长ｙ一路，即以ｙ为终点的路中最长者．那么且对也是最长ｙ一路．利用该简单原理证明：对于２－连通非Ｈａｍｉｌｔｏｎ图Ｇ的任一顶点ｙ．存在某最长ｙ－路Ｐ（ｘ，ｙ）使ｄ（ｘ）较大．据此直接推出关于周长的范更华定理等重要结果。
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| 关 键 词： | 最长y－路，最长路原理，（隐）次条件，周长 |
LONGEST PATH PINCIPLE AND PATHS NAD CYCLES IN GRAPHS |
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| Gao Jingzhen. LONGEST PATH PINCIPLE AND PATHS NAD CYCLES IN GRAPHS[J]. Journal of Shandong Normal University(Natural Science), 1995, 0(1) |
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| Authors: | Gao Jingzhen |
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| Abstract: | et(where)be a longest y-path in graph G,Then N(vo),anda longest y-path,too, for any Using this simple principle ,we show that for any vertex y of a 2-connected nonhamiltonian graph G ,there exists a longest y-path P(x,y)such that d(x) is relatively large. Based on those results several important theorems including Fan's on thecircurnference of a graph are straightforwardly deduced. |
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| Keywords: | longext y-path longest path principle (implicit)degree condition circumference |
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