On k-Star Arboricity of Graphs  

作　　者：陶昉昀 林文松 

机构地区：[1]Department of Mathematics,Southeast University [2]College of Science,College of Science,Nanjing Forestry University

出　　处：《Journal of Donghua University(English Edition)》2014年第3期335-338,共4页东华大学学报（英文版）

基　　金：National Natural Science Foundation of China(No.10971025)

摘　　要：A star forest is a forest whose components are stars. The star arboricity of a graph G,denoted by sa（ G）,is the minimum number of star forests needed to decompose G. Let k be a positive integer. A k-star forest is a forest whose components are stars of order at most k ＋ 1. The k-star arboricity of a graph G,denoted by sak（ G）,is the minimum number of k-star forests needed to decompose G. In this paper,it is proved that if any two vertices of degree 3 are nonadjacent in a subcubic graph G then sa2（ G） ≤2.For general subcubic graphs G, a polynomial-time algorithm is described to decompose G into three 2-star forests. For a tree T and[Δ k, T）/k]t≤ sak（ T） ≤[Δ（ T）- 1/K]＋1,where Δ（ T） is the maximum degree of T.kMoreover,a linear-time algorithm is designed to determine whether sak（ T） ≤m for any tree T and any positive integers m and k.A star forest is a forest whose components are stars. The star arboricity of a graph G,denoted by sa( G),is the minimum number of star forests needed to decompose G. Let k be a positive integer. A k-star forest is a forest whose components are stars of order at most k + 1. The k-star arboricity of a graph G,denoted by sak( G),is the minimum number of k-star forests needed to decompose G. In this paper,it is proved that if any two vertices of degree 3 are nonadjacent in a subcubic graph G then sa2( G) ≤2.For general subcubic graphs G, a polynomial-time algorithm is described to decompose G into three 2-star forests. For a tree T andΔ( a positive integer k, T)it is proved that≤ sakk( T) ≤Δ( T)- 1+ 1,where Δ( T) is the maximum degree of T.kMoreover,a linear-time algorithm is designed to determine whether sak( T) ≤m for any tree T and any positive integers m and k.

关 键 词：star arboricity k-star arboricity linear k-arboricity cubic graphs subcubic graphs 

分 类 号：O157.5[理学—数学] O177.91[理学—基础数学]