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图G的全图T(G)是以V(G)∪E(G)为顶点集的一个图,其中两个顶点相邻当且仅当它们在图G中对应的元素是相邻或关联的.图G的全荫度ρ"(G)是将其全图的顶点集V(T(G))划分为最少的子集数,使得每个子集在全图中的导出子图是一个森林.列表全荫度硝(G)是全荫度概念的列表染色的版本.本文证明了:(1)对完全图‰,ρ"(Kn)=「(n+1)/2];(2)对完全二部图Kn,n,ρ"(Kn,n)=「(n+2)/2];(3)对Halin图G,ρl"(G)≤「(△(G)+2)/2]. 相似文献
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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. 相似文献
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