关于超图圈分解的研究

On Decompostition of Hypergraphs into Cycles

现代科学技术的进步和计算机以及信息等相关学科的快速发展,使得离散数学中的组合设计、图论、超图、网络理论以及编码设计等领域的研究内容越来越丰富、充实,同时,提出了许多具有重要理论意义和应用前景的新问题.本文中我们用组合数学与数论的方法构造超图K3n所有边的一种划分方法,在此划分的基础上根据边与边之间连接的需要,定义超图的圈模型,进而给出n≠3k时超图K3n的不同长度的圈的分解,和n=3k时超图K3n-H(k,k)的不同长度的圈的分解,并用此方法进一步研究超图K3q(q为素数)的Hamilton圈分解.

Fast progress of modern science and technology and the disciplines which relate graph theory such as computer and information science, makes the research contents of combinatorial design,graph theory, hypergraph, network theory and design of code in discrete mathematics increasingly enrich, at the same time, puts forward many new problems which have important theoretical significance and prospect of application. In this paper, Ⅰ construct a classification method on all edges of hypergraph K^3 using the methods of combinatorial mathematics and number theory, based on these classification, defines hypergraphs＇ circle model according to the joint need between edge and edge,and study the circle decomposition of different length of hypergraph Kn^3 for n≠3k, and the circle decomposition of different length of hypergraph Kn^3 - H（k, k） for n = 3k, further discuss Hamilton circle decomposition of hypergraph Kq^3（q is a prime）.