Graphs Without Large Apples and the Maximum Weight Independent Set Problem

被引:0
|
作者
Vadim V. Lozin
Martin Milanič
Christopher Purcell
机构
[1] University of Warwick,DIMAP and Mathematics Institute
[2] University of Primorska,undefined
[3] UP IAM,undefined
[4] University of Primorska,undefined
[5] UP FAMNIT,undefined
来源
Graphs and Combinatorics | 2014年 / 30卷
关键词
Claw-free graphs; Chordal graphs; Independent set; polynomial algorithm;
D O I
暂无
中图分类号
学科分类号
摘要
An appleAk is the graph obtained from a chordless cycle Ck of length k ≥ 4 by adding a vertex that has exactly one neighbor on the cycle. The class of apple-free graphs is a common generalization of claw-free graphs and chordal graphs, two classes enjoying many attractive properties, including polynomial-time solvability of the maximum weight independent set problem. Recently, Brandstädt et al. showed that this property extends to the class of apple-free graphs. In the present paper, we study further generalization of this class called graphs without large apples: these are (Ak, Ak+1, . . .)-free graphs for values of k strictly greater than 4. The complexity of the maximum weight independent set problem is unknown even for k = 5. By exploring the structure of graphs without large apples, we discover a sufficient condition for claw-freeness of such graphs. We show that the condition is satisfied by bounded-degree and apex-minor-free graphs of sufficiently large tree-width. This implies an efficient solution to the maximum weight independent set problem for those graphs without large apples, which either have bounded vertex degree or exclude a fixed apex graph as a minor.
引用
收藏
页码:395 / 410
页数:15
相关论文
共 50 条
  • [1] Graphs Without Large Apples and the Maximum Weight Independent Set Problem
    Lozin, Vadim V.
    Milanic, Martin
    Purcell, Christopher
    [J]. GRAPHS AND COMBINATORICS, 2014, 30 (02) : 395 - 410
  • [2] An algorithm for the maximum weight independent set problem on outerstring graphs
    Keil, J. Mark
    Mitchell, Joseph S. B.
    Pradhan, Dinabandhu
    Vatshelle, Martin
    [J]. COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2017, 60 : 19 - 25
  • [3] ON THE MAXIMUM WEIGHT INDEPENDENT SET PROBLEM IN GRAPHS WITHOUT INDUCED CYCLES OF LENGTH AT LEAST FIVE
    Chudnovsky, Maria
    Pilipczuk, Marcin
    Pilipczuk, Michal
    Thomasse, Stephan
    [J]. SIAM JOURNAL ON DISCRETE MATHEMATICS, 2020, 34 (02) : 1472 - 1483
  • [4] Exactly Solving the Maximum Weight Independent Set Problem on Large Real-World Graphs
    Lamm, Sebastian
    Schulz, Christian
    Strash, Darren
    Williger, Robert
    Zhang, Huashuo
    [J]. 2019 PROCEEDINGS OF THE MEETING ON ALGORITHM ENGINEERING AND EXPERIMENTS, ALENEX, 2019, : 144 - 158
  • [5] Maximum weight k-independent set problem on permutation graphs
    Saha, A
    Pal, M
    [J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2003, 80 (12) : 1477 - 1487
  • [6] The maximum independent set problem in planar graphs
    Alekseev, Vladimir E.
    Lozin, Vadim
    Malyshev, Dmitriy
    Milanic, Martin
    [J]. MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE 2008, PROCEEDINGS, 2008, 5162 : 96 - +
  • [7] On the Maximum Independent Set Problem in Graphs of Bounded Maximum Degree
    Ngoc C. Lê
    Trung Tran
    [J]. Acta Mathematica Vietnamica, 2020, 45 : 463 - 475
  • [8] On the Maximum Independent Set Problem in Graphs of Bounded Maximum Degree
    Le, Ngoc C.
    Trung Tran
    [J]. ACTA MATHEMATICA VIETNAMICA, 2020, 45 (02) : 463 - 475
  • [9] SEQUENTIAL AND PARALLEL ALGORITHMS FOR THE MAXIMUM-WEIGHT INDEPENDENT SET PROBLEM ON PERMUTATION GRAPHS
    YU, MS
    TSENG, LY
    CHANG, SJ
    [J]. INFORMATION PROCESSING LETTERS, 1993, 46 (01) : 7 - 11
  • [10] PTAS for maximum weight independent set problem with random weights in bounded degree graphs
    Gamarnik, David
    Goldberg, David
    Weber, Theophane
    [J]. PROCEEDINGS OF THE TWENTY-FIRST ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, 2010, 135 : 268 - 278