A k-tree is a tree with maximum degree at most k. In this paper, we give a sharp degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than t, where 1≤t≤k.We denote ...A k-tree is a tree with maximum degree at most k. In this paper, we give a sharp degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than t, where 1≤t≤k.We denote by σ_k(G) the minimum value of the degree sum of k independent vertices in a graph G. Let k≥2,s≥0 and 1≤t≤k be integers, and suppose G is an(s + 1)-connected graph with σ_k(G)≥|G|+(k-t)s-1.Then for any s specified vertices, G contains a spanning k-tree in which every specified vertex has degree at most t. This improves a result obtained by Matsuda and Matsumura.展开更多
基金Partially supported by National Natural Science Foundation of China(No.11771172)key scientific and technological project of higher education of Henan Province(No.19A110019)+1 种基金Science and technology innovation fund of Henan Agricultural University(No.KJCX2019A15)Partially supported by the Ph D Research Foundation of Henan Agricultural University(No.30500614)
文摘A k-tree is a tree with maximum degree at most k. In this paper, we give a sharp degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than t, where 1≤t≤k.We denote by σ_k(G) the minimum value of the degree sum of k independent vertices in a graph G. Let k≥2,s≥0 and 1≤t≤k be integers, and suppose G is an(s + 1)-connected graph with σ_k(G)≥|G|+(k-t)s-1.Then for any s specified vertices, G contains a spanning k-tree in which every specified vertex has degree at most t. This improves a result obtained by Matsuda and Matsumura.
