On a Spanning K-tree Containing Specified Vertices in a Graph

被引：0
|
作者：
Song, Fei-fei [1 ]
Hu, Zhi-quan [2 ]
机构：
[1] Henan Agr Univ, Dept Informat & Computat Sci, Zhengzhou 450002, Peoples R China
[2] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China
来源：
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES | 2019年 / 35卷 / 04期
基金：
中国国家自然科学基金;
关键词：
spanning tree; k-tree; (s+1)-connected graphs; degree sum condition; specified vertices;
D O I：
10.1007/s10255-019-0864-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 sigma(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 sigma(k)(G) >= divide G divide + (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.
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页码：919 / 923
页数：5
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