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...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.展开更多
基金National Natural Science Foundation of China(No.10971025)
文摘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.
