Linear-vertex kernel for the problem of packing r-stars into a graph without long induced paths

被引：3

作者：

Barbero, Florian ^{[1
]}

Gutin, Gregory ^{[2
]}

Jones, Mark ^{[2
]}

Sheng, Bin ^{[2
]}

Yeo, Anders ^{[3
,4
]}

机构：

[1] Lab Informat Robot & Microelect Montpellier, 161 Rue Ada, F-34095 Montpellier 5, France

[2] Univ London, Dept Comp Sci, Royal Holloway, Egham TW20 0EX, Surrey, England

[3] Singapore Univ Technol & Design, Engn Syst & Design, Singapore, Singapore

[4] Univ Johannesburg, Dept Math, ZA-2006 Auckland Pk, South Africa

来源：

INFORMATION PROCESSING LETTERS | 2016年 / 116卷 / 06期

关键词：

Graph algorithms; Packing; Stars; Kernel; Fixed-parameter tractability;

D O I：

10.1016/j.ipl.2016.01.007

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Let integers r >= 2 and d >= 3 be fixed. Let g(d) be the set of graphs with no induced path on d vertices. We study the problem of packing k vertex-disjoint copies of K-1,K-r, (k >= 2) into a graph G from parameterized preprocessing, i.e., kernelization, point of view. We show that every graph G epsilon g(d) can be reduced, in polynomial time, to a graph G' epsilon g(d) with 0 (k) vertices such that G has at least k vertex-disjoint copies of K-1,K-r if and only if G' has. Such a result is known for arbitrary graphs G when r = 2 and we conjecture that it holds for every r >= 2. 2016 Elsevier B.V. All rights reserved.

引用

页码：433 / 436

页数：4