【摘要】：設X是完全圖Kn的點集,C是Kn中一些邊不交的k-圈的集合,L(稱為邊剩余)是Kn的邊集的子集,若L和C中無公共邊,且他們的所有邊恰好是Kn邊集的一個劃分,則稱三元組(x,C,L)是一個k-圈填充,記為k-CP(m)設(x,c,L)是一個k-圈填充,c中[n/k]個不相交的k-圈稱為Kn的一個幾乎平行類.當n三0(mod k)時,稱幾乎平行類為平行類.設(x,C,L)為一個k-CP(n),若C可以劃分為一些幾乎平行類,則稱(x,C,L)為幾乎可分解的,記為k-ARCP(n)進一步,設(x,C,L)是一個幾乎可分解的k-圈填充,若c中幾乎平行類個數(shù)達到最大,則稱(X,C,L)是最大幾乎可分解的k-圈填充,記為k-MARCP(n).記D(n,k)為k-MARCP(n)中幾乎平行類的個數(shù).當k=3,4,5時,D(n,k)的值已經(jīng)完全確定.當n三1(mod 2k)且k∈{6,8,10,14)∪{m:5≤m≤49,m(?)1 (mod 2)}時,D(n,k)的值也已經(jīng)基本確定.本文主要確定了D(n,6)的值.
[Abstract]:Let X be a point set of a complete graph Kn, C be a set of k-cycles with disjoint edges called edge residuals in Kn) be a subset of the edge set of Kn if there are no common edges in L and C, and all their edges happen to be a partition of the Kn edge set. Then the triple (XL) is a k-cycle filled, denoted as k-CP (m) let (XL) be a k-cycle padding, and [n / k] disjoint k-cycles in c is called an almost parallel class of Kn. When n 30 (mod k), almost parallel class is called parallel class. If C can be divided into some almost parallel classes, then (XG C L) is almost decomposable, which is denoted as k-ARCP (n) further, let (XG C) be (XG C), if C can be divided into some almost parallel classes, let (XG C) be called almost decomposable. L) is an almost decomposable k- cycle filling. If the number of almost parallel classes in c reaches the maximum, then (XG CU L) is the largest almost decomposable kcycle filling, denoted as k-MARCP (n). Let D (NK) be the number of almost parallel classes in k-MARCP (n). The value of, D (NK has been fully determined when KG is 4, 5. When n 3 1 (mod 2k) and k 鈭，

本文編號：2309383