Star number and star arboricity of a complete multigraph
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- 作者：Chiang Lin and Tay-Woei Shyu
- 关键词：decomposition ; star arboricity ; star forest ; complete multigraph
- 刊名：Czechoslovak Mathematical Journal
- 出版年：2006
- 出版时间：September, 2006
- 年：2006
- 卷：56
- 期：3
- 页码：961-967
- 全文大小：118 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics
Analysis
Convex and Discrete Geometry
Ordinary Differential Equations
Mathematical Modeling and IndustrialMathematics - 出版者：Springer Netherlands
- ISSN：1572-9141
文摘
Let G be a multigraph. The star number s(G) of G is the minimum number of stars needed to decompose the edges of G. The star arboricity sa(G) of G is the minimum number of star forests needed to decompose the edges of G. As usual λK n denote the λ-fold complete graph on n vertices (i.e., the multigraph on n vertices such that there are λ edges between every pair of vertices). In this paper, we prove that for n ⩾ 2 s(lKn ) = { \frac12(l+ 1)n - 1 if lis odd,\frac12ln if lis even, s(\lambda K_n ) = \left\{ {_{\frac{1}{2}(\lambda + 1)n - 1 if \lambda is odd,}^{\frac{1}{2}\lambda n if \lambda is even,} } \right.