图K_nH_((5n/2)-4)的升分解

THE ASCENDING SUBGRAPH DECOMPOSITION OF K_n-H_((5N/2)-4)

Ａｌａｖｉ等人给出了图的升分解的概念并猜测任何一个有正数条边的图都可以升分解．Ｆａｕｄｒｅｅ等１９８７年证明了当完全图Ｋｎ的子图Ｈ至多有ｎ—１条边时，Ｋｎ－Ｈ可以升分解．马克杰等１９９７年证明了当Ｈ至多含有ｎ条边时，Ｋｎ－Ｈ可以升分解．作者１９９９年证明了当Ｈ的边数小于３ｎ／２时，Ｋｎ－Ｈ可以升分解．本文将证明当Ｈ的边数小于（５ｎ／２）－４时Ｋｎ－Ｈ有升分解．

Alavi and his collaborators defined the concept of ascending subgraph de-composition of a graph and conjectured that every graph with positive size has an ascending subgraph decomposition. In 1987, Faudree et al. proved that Kn- Hn-1 has a star ascending subgraph decomposition, where Kn is the complete graph with order n and Hn-1 is a subgraph of Kn with size n-1. In 1997, Ma Kejie and Chen Huaitang proved that Kn- Hn has a ascending subgraph decomposition when the size of Hn is not greater than n. In 1999, Zhao Guangfeng et al. proved Kn- H has a comet ascending subgraph decomposition when the size of H is less than 3n/2 This paper has proved that Kn- H has a comet ascending subgraph decomposition when the size of H is less than 5n/2- 4.