Critical hereditary graph classes: a survey

被引：0
|
作者：
D. S. Malyshev
P. M. Pardalos
机构：
[1] National Research University Higher School of Economics,
[2] University of Florida,undefined
来源：
Optimization Letters | 2016年 / 10卷
关键词：
Computational complexity; Polynomial-time algorithm ; Hereditary graph class; Independent set problem; Dominating set problem; Coloring problem; List edge-ranking problem;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The task of complete complexity dichotomy is to clearly distinguish between easy and hard cases of a given problem on a family of subproblems. We consider this task for some optimization problems restricted to certain classes of graphs closed under deletion of vertices. A concept in the solution process is based on revealing the so-called “critical” graph classes, which play an important role in the complexity analysis for the family. Recent progress in studying such classes is presented in the article.
引用
收藏
页码：1593 / 1612
页数：19
相关论文
共 50 条
  • [21] Critical elements in combinatorially closed families of graph classes
    Malyshev D.S.
    Journal of Applied and Industrial Mathematics, 2017, 11 (1) : 99 - 106
  • [22] On some graph classes related to perfect graphs: A survey
    Bonomo-Braberman, Flavia
    Duran, Guillermo
    Safe, Martin D.
    Wagler, Annegret K.
    DISCRETE APPLIED MATHEMATICS, 2020, 281 : 42 - 60
  • [23] Characterizations of graph classes via convex geometries: A survey
    Dourado, Mitre C.
    Gutierrez, Marisa
    Protti, Fabio
    Sampaio, Rudini
    Tondato, Silvia
    DISCRETE APPLIED MATHEMATICS, 2025, 360 : 246 - 257
  • [24] HADWIGER'S CONJECTURE FOR SOME HEREDITARY CLASSES OF GRAPHS: A SURVEY
    Cameron, Kathie
    Vuskovic, Kristina
    BULLETIN OF THE EUROPEAN ASSOCIATION FOR THEORETICAL COMPUTER SCIENCE, 2020, 131 (131): : 1 - 18
  • [25] A SURVEY OF RESULTS ON A GRAPH AND ITS COMPLEMENT WITH SPECIFIED HEREDITARY PROPERTIES
    DINY, DA
    HARARY, F
    MCMORRIS, FR
    ARS COMBINATORIA, 1985, 20B : 193 - 205
  • [26] Some Classes Of 3-γc- critical Graph
    Yu, Zhen
    Liu, Hongmei
    FIFTH INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS AND KNOWLEDGE DISCOVERY, VOL 3, PROCEEDINGS, 2008, : 627 - 629
  • [27] Some new hereditary classes where graph coloring remains NP-hard
    Schindl, D
    DISCRETE MATHEMATICS, 2005, 295 (1-3) : 197 - 202
  • [28] Efficient Solvability of the Weighted Vertex Coloring Problem for Some Two Hereditary Graph Classes
    Razvenskaya O.O.
    Malyshev D.S.
    Journal of Applied and Industrial Mathematics, 2021, 15 (01) : 97 - 117
  • [29] On graph isomorphism for restricted graph classes
    Koebler, Johannes
    LOGICAL APPROACHES TO COMPUTATIONAL BARRIERS, PROCEEDINGS, 2006, 3988 : 241 - 256
  • [30] Semisimple Classes, Radical Classes and Strongly Hereditary Radical Classes of Groups
    Zhang, Zhirang
    Chen, Shengsheng
    Li, Xuemei
    SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2014, 38 (03) : 459 - 470
12345