超图的分解及其应用.pdf

摘要随着现在科学技术的进步与发展,离散数学中的图论,超图,组合设计,编码设计等领域的研究内容越来越丰富。超图作为离散数学中最一般的结构,对它的研究也有重要的意义。 Hamiltonian圈的基础上,主要做了以下研究和讨论,详细内容如下: 第一章简单的介绍了一般图与超图中与研究内容相关的基本概念,及关于超图分解问题研究的国内外进展情况。,针对完全3-一致超图的Hamiltonian圈分解设计了算法。当以三1(mod61时,, 得到了/-/≤;当,7兰2,4,5(rood 6)时,在边划分的基础上,结合差分模式(Bailey。Stevens)与扩展的差分模式()的方法,得到了胛≤,这一结果将t/≤32所有可能的值()扩展到玎≤46,行≠43所有可能的值;, 。,,. 圈的定义,。第四章的第一部分研究了圈分解在设计中的应用;第二部分直接利用超图的边划分研究卜设计的大集问题。关键词:超图;Hamiltonian圈;;圈分解;差分模式;f一设计:大集 Hyoergraohs oositions and itsApplications ?l l^ Abst ract Withdeveloping ofmodem science and technology,the research contents ofgraph theory,binatorial design,coding design in discrete mathematics increasingly beregarded as the most general structure indiscrete research ithave important thispaper,on the basicofdefinition ofHamiltonian cycle by Katona—Kierstead and -,mainly make the following researchand discussion,the detailsare asfollows: The firstchapter simply introduces the basic concepts of general graphs and hypergraphs,and theresearch development ofhypergraphs positions. Inthe second chapter,the firstpart improves Hamiltonian cycle structure plete 3-uniform hypergraphs,and designs algorithm for Hamiltonian cycle positions plete 3-uniform n三1(mod6),we obtain Hamiltoniancycle positions plete 3-uniform hypergraphs for 胛≤37 by method ofMeszka- n兰2,4,5(mod 6),on basicofedge-bine with difference method and an extension ofthe difference method,obtain Hamiltonian cycle positions plete 3-uniform hypergraphs for n≤ articleimproves resultsofHamiltonian cycle positions from alladmissible n≤32 fMeszka—Rosa’S paper)to alladmissible行≤46,n≠ second part defines difference