【摘要】 J.C Bermond在1989年已证"Abel群上4度Cayley图可分解为两个边互不相交的Hamilton圈的并",其分解方法首先要对简化图进行分解后才能实现,产生一定局限性,不但数目少,而且方法也比较繁杂.4度Cayley图的Hamilton圈分解的新方法与理论证明是利用Hamilton圈上"单向通道"的"离合"理论和方法,给出了Abel群上4度Cayley图的Hamilton圈分解方案和理论证明.对新方法分解方案多且简明快捷的特点作进一步研究,并对两种方法进行比较,得到"H操作法"分解方案,超过Bermond分解方案的6倍(含Bermond分解方案).更多还原

【Abstract】 In 1989,the theory that a Cayley graph of degree 4 on Abel group is the union of two uncorrelated Hamiltonian loop was discussed by J.C Bermond.The theory was limited,because the decomposition method was finstly realized by decomposition of simplified graph.The decomposition scheme is less quantities and the method is very complicated.The new method and theoretical confirmation on Hamiltonian decomposition of cayley graphs of degree 4,basedon the theory that the Hamiltonian decomposition of Cayley graph of degree 4 on commutative group(H operative method),has been proved and its multicommodity has been discussed.In this paper,we compare the Hamiltonian decomposition of Cayley graph and "Hamilton"method and obtain,"the method of H operation".The decomposition scheme(containing the Bermond’s scheme) is 6 times more than Bermond’s scheme.更多还原