论k阶最长路

论ｋ阶最长路秦裕瑗（武汉钢铁学院管理工程系４３００８１）ＯｎＬｏｎｇｅｓｔＰａｔｈｓｏｆｔｈｅｋ－ｔｈＯｒｄｅｒＱｉｎＹｕｙｕａｎ（ＷｕｈａｎＩｒｏｎａｎｄＳｔｅｅｌＵｎｉｖｅｒｓｉｔｙ４３００８１）ＡｂｓｔｒａｃｔＴｈｅ［１］ｇｉｖｅｓａｎａｌｇｏ...

On Longest Paths of the k-th Order

The [1] gives an algorithm with computational complexity of the second order for finding the longest path of the k-th order in networks where k is a prescribed non-negative in-teger. This article discusses fundamental properties among longest paths of the k-th order.It also constructively proves that in a complete network with n vertices, it needs only n²/ 4 mutu-ally independent paths from the initial vertex to the end vertes of the network to cover all the arcs of the networ.