The study of decomposing λKn(m) into most cycles
| Autor: | Nan-Hua Jhuang, 莊柟樺 |
|---|---|
| Rok vydání: | 2001 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 89 A graph is to be a complete graph Kn if the graph has n points and there is an edge joining any two points. A complete n-partite graph is a graph with n partite sets,m1,m2,….,mn points, respectively. There is an edge joining any two points which belong to different parts, and no edge connected any two points in the same part. If each part has the same number of points, say m, can be denoted by Kn(m). λKn(m) is a λ-fold complete n-partite graph, each part has m points. A packing of G with triangles is an ordered triple (S,H,L),where S is the vertex set of G. H is a collection of edge-disjoint triangles of G and L is the set of edges in G which do not belong to any triangle of H. The set of edges in L is called the leave of the packing H of G. If the number of elements in H is as large as possible, or equivalently the number of elements in L is as small as possible then the packing of G with triangles is said to be maximum, and L is a minimum leave. In this thesis, we obtain the maximum packing and the minimum leave of lKn with triangles for λ,n are integers and λ>1, n>2. By using the results of the maximum packing of lKn with triangles, we try to decompose λKn(m) into most cycles. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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