完全图的最大几乎可分解的6-圈填充
发布时间：2018-11-04 09:12
【摘要】：设X是完全图Kn的点集,C是Kn中一些边不交的k-圈的集合,L(称为边剩余)是Kn的边集的子集,若L和C中无公共边,且他们的所有边恰好是Kn边集的一个划分,则称三元组(x,C,L)是一个k-圈填充,记为k-CP(m)设(x,c,L)是一个k-圈填充,c中[n/k]个不相交的k-圈称为Kn的一个几乎平行类.当n三0(mod k)时,称几乎平行类为平行类.设(x,C,L)为一个k-CP(n),若C可以划分为一些几乎平行类,则称(x,C,L)为几乎可分解的,记为k-ARCP(n)进一步,设(x,C,L)是一个几乎可分解的k-圈填充,若c中几乎平行类个数达到最大,则称(X,C,L)是最大几乎可分解的k-圈填充,记为k-MARCP(n).记D(n,k)为k-MARCP(n)中几乎平行类的个数.当k=3,4,5时,D(n,k)的值已经完全确定.当n三1(mod 2k)且k∈{6,8,10,14)∪{m:5≤m≤49,m(?)1 (mod 2)}时,D(n,k)的值也已经基本确定.本文主要确定了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，
本文编号：2309383
[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，
本文编号：2309383
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