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.
引用
收藏
页码：919 / 923
页数：5
相关论文
共 50 条
  • [11] Approximating the Spanning k-Tree Forest Problem
    Liao, Chung-Shou
    Zhang, Louxin
    FRONTIERS IN ALGORITHMICS, PROCEEDINGS, 2009, 5598 : 293 - +
  • [12] Graph partition into paths containing specified vertices
    Kawarabayashi, K
    DISCRETE MATHEMATICS, 2002, 248 (1-3) : 271 - 277
  • [13] On a spanning tree with specified leaves in a bipartite graph
    Tsugaki, Masao
    Yamashita, Tomoki
    AUSTRALASIAN JOURNAL OF COMBINATORICS, 2020, 77 : 69 - 86
  • [14] EQUALITY OF CYCLES CONTAINING SPECIFIED VERTICES OF A GRAPH
    MAAMOUN, M
    DISCRETE MATHEMATICS, 1981, 34 (02) : 145 - 152
  • [15] A Sufficient Condition for a Graph to Have a k-tree
    Aung Kyaw
    Graphs and Combinatorics, 2001, 17 : 113 - 121
  • [16] A sufficient condition for a graph to have a k-tree
    Kyaw, A
    GRAPHS AND COMBINATORICS, 2001, 17 (01) : 113 - 121
  • [17] Finding the maximum common subgraph of a partial k-tree and a graph with a polynomially bounded number of spanning trees
    Yamaguchi, A
    Aoki, KF
    Mamitsuka, H
    INFORMATION PROCESSING LETTERS, 2004, 92 (02) : 57 - 63
  • [18] Finding the maximum common subgraph of a partial k-tree and a graph with a polynomially bounded number of spanning trees
    Yamaguchi, A
    Mamitsuka, H
    ALGORITHMS AND COMPUTATION, PROCEEDINGS, 2003, 2906 : 58 - 67
  • [19] Maximizing the Index of Signed Complete Graphs Containing a Spanning Tree with k Pendant Vertices
    Li, Dan
    Yan, Minghui
    Teng, Zhaolin
    AXIOMS, 2024, 13 (08)
  • [20] Connectivity of the graph induced by contractible edges of a k-tree
    Qin, Chengfu
    Guo, Litao
    Huang, Lexian
    APPLIED MATHEMATICS AND COMPUTATION, 2019, 353 : 1 - 6
12345