Abstract: Theorem 2. If hKn has a Hamilton Ck-bowtie decomposition, then (sA)Kn, has a Hamilton Ck-bowtie decomposition for every s. Let K, denote the complete graph of n vertices. The complete multi-graph AKn is the complete graph Kn in which every edge is taken A times. Let Ck be the k-cycle (or the cycle on k vertices). The Ckbowtie is a graph of 2 edge-disjoint Ck's with a common vertex and the common vertex is called the center of the Ck-bowtie. In particular, a Ck-bowtie satisfying n = 2(k 1) + 1 is called the Hamilton Ckbowtie because the Ck-bowtie spans AKn,. When AKn,is decomposed into edge-disjoint sum of Hamilton Ck-bowties, we say that AKn has a Hamilton Ck-bowtie decomposition. This Hamilton Ckbowtie decomposition of AK,„ is called a Hamilton Ck-bowtie design.
Publication Year: 2008
Publication Date: 2008-09-01
Language: en
Type: article
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