On the k-path vertex cover of some graph products

被引：27
|
作者：
Jakovac, Marko
Taranenko, Andrej [1 ]
机构：
[1] Univ Maribor, Fac Nat Sci & Math, SI-2000 Maribor, Slovenia
来源：
DISCRETE MATHEMATICS | 2013年 / 313卷 / 01期
关键词：
k-path vertex cover; Vertex cover; Dissociation number; Independence number; Graph products; INDEPENDENCE NUMBER; DISSOCIATION NUMBER; BIPARTITE GRAPHS; TERMS;
D O I：
10.1016/j.disc.2012.09.010
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A subset S of vertices of a graph G is called a k-path vertex cover if every path of order kin G contains at least one vertex from S. Denote by psi(k)(G) the minimum cardinality of a k-path vertex cover in G. In this paper, improved lower and upper bounds for psi(k) of the Cartesian and the strong product of paths are derived. It is shown that for psi(3) those bounds are tight. For the lexicographic product bounds are presented for psi(k), moreover psi(2) and psi(3) are exactly determined for the lexicographic product of two arbitrary graphs. As a consequence the independence and the dissociation number of the lexicographic product are given. (C) 2012 Elsevier B.V. All rights reserved.
引用
收藏
页码：94 / 100
页数：7
相关论文
共 50 条
  • [1] On the vertex k-path cover
    Bresar, Bostjan
    Jakovac, Marko
    Katrenic, Jan
    Semanisin, Gabriel
    Taranenko, Andrej
    DISCRETE APPLIED MATHEMATICS, 2013, 161 (13-14) : 1943 - 1949
  • [2] PTAS for minimum k-path vertex cover in ball graph
    Zhang, Zhao
    Li, Xiaoting
    Shi, Yishuo
    Nie, Hongmei
    Zhu, Yuqing
    INFORMATION PROCESSING LETTERS, 2017, 119 : 9 - 13
  • [3] On a relation between k-path partition and k-path vertex cover
    Brause, Christoph
    Krivos-Bellus, Rastislav
    DISCRETE APPLIED MATHEMATICS, 2017, 223 : 28 - 38
  • [4] Minimum k-path vertex cover
    Bresar, Bostjan
    Kardos, Frantisek
    Katrenic, Jan
    Semanisin, Gabriel
    DISCRETE APPLIED MATHEMATICS, 2011, 159 (12) : 1189 - 1195
  • [5] A Survey on the k-Path Vertex Cover Problem
    Tu, Jianhua
    AXIOMS, 2022, 11 (05)
  • [6] On the weighted k-path vertex cover problem
    Bresar, B.
    Krivos-Bellus, R.
    Semanisin, G.
    Sparl, P.
    DISCRETE APPLIED MATHEMATICS, 2014, 177 : 14 - 18
  • [7] On the minimum vertex k-path cover of trees
    Lemanska, Magdalena
    UTILITAS MATHEMATICA, 2016, 100 : 299 - 307
  • [8] The k-path vertex cover of rooted product graphs
    Jakovac, Marko
    DISCRETE APPLIED MATHEMATICS, 2015, 187 : 111 - 119
  • [9] Complexity of the Maximum k-Path Vertex Cover Problem
    Miyano, Eiji
    Saitoh, Toshiki
    Uehara, Ryuhei
    Yagita, Tsuyoshi
    van der Zanden, Tom C.
    IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2020, E103A (10) : 1193 - 1201
  • [10] Complexity of the Maximum k-Path Vertex Cover Problem
    Miyano, Eiji
    Saitoh, Toshiki
    Uehara, Ryuhei
    Yagita, Tsuyoshi
    van der Zanden, Tom C.
    WALCOM: ALGORITHMS AND COMPUTATION, WALCOM 2018, 2018, 10755 : 240 - 251
12345