The study of Decomposing a complete multipartite graph into pentagons

• Main Authors: Wei-Hsuan Liao, 廖威絢
• Other Authors: Chin-Mei Kau Fu
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/80183608379753430640

碩士 === 淡江大學 === 數學學系 === 90 === A complete k-partite graph is a graph whose vertices can be partitioned into k disjoint nonempty sets, and there are no edges within two vertices which are in the same set, and every edge joins two vertices which are in different partite sets. A complete four-partite graph with n vertices in each partite set, then we will denote it by K4(n). A pentagon is a 5-cycle. K4(n) can be decomposed into pentagons if the edges of K4(n) can be partitioned into edge-disjoint 5-cycles. If the edges of K4(n) can not be completely partitioned into edge-disjoint 5-cycles, we will call the graph with left edges a remaining graph which derived from a packing of K4(n) with pentagons. In this thesis we will prove that the necessary and sufficient conditions for decomposing K4(n) into pentagons are 10|n and prove that K2n,2n,2n,8n can be decomposed into pentagons. In the last section, we obtain the remaining graphs of packing K4(n) into pentagons when n<10.