关于3-正则4-可序图无限类的构造

An Infinite Contruction of 3Regular 4Ordered Graphs

LenhardNg(1997)给出k-可序(kordered)哈密尔顿图的定义,并证明了每一个(k+1)Hamilton-连通图都是k-可序哈密尔顿图.FaudreeJR(2000)将k-可序哈密尔顿图的定义改进为k-可序图.根据LenhardNg提出的开问题:是否存在3-正则4-可序哈密尔顿图的无限类,以及FaudreeJR给出的可序图的定义,构造了3-正则4-可序图的无限类.

Lenhard Ng (1997) gave the definition of k-ordered Hamilton graphs and proved that every (k+1)-Hamilton-connected graph is the k-ordered Hamilton graph.Faudree J R (2000) developed this definition into a k-ordered graph.According to the open question proposed by Lenhard Ng,namely,whether there exists an infinite class of 3-regular 4-ordered graphs or not,and the ordered graph definition given by Faudree J R,an infinite class of 3-regular 4-ordered graphs were constructed.