Maximum independent sets in 3-and 4-regular Hamiltonian graphs

被引：22

作者：

Fleischner, Herbert ^{[2
]}

Sabidussi, Gert ^{[1
]}

Sarvanov, Vladimir I. ^{[3
]}

机构：

[1] Univ Montreal, Dept Math & Stat, Montreal, PQ H3C 3J7, Canada

[2] Vienna Univ Technol, Inst Informat Syst, A-1040 Vienna, Austria

[3] Natl Acad Sci Belarus, Inst Math, Dept Combinatorial Models & Algorithms, Minsk 220072, BELARUS

来源：

DISCRETE MATHEMATICS | 2010年 / 310卷 / 20期

基金：

加拿大自然科学与工程研究理事会;

关键词：

NP-completeness; Maximum independent set; 3-or 4-regular graph; Planar graphs;

D O I：

10.1016/j.disc.2010.05.028

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Smooth 4-regular Hamiltonian graphs are generalizations of cycle-plus-triangles graphs. While the latter have been shown to be 3-choosable, 3-colorability of the former is NP-complete. In this paper we first show that the independent set problem for 3-regular Hamiltonian planar graphs is NP-complete, and using this result we show that this problem is also NP-complete for smooth 4-regular Hamiltonian graphs. We also show that this problem remains NP-complete if we restrict the problem to the existence of large independent sets (i.e., independent sets whose size is at least one third of the order of the graphs). (c) 2010 Elsevier B.V. All rights reserved.

引用

页码：2742 / 2749

页数：8

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