The complexity of clique graph recognition

被引：20

作者：

Alcon, Liliana

Faria, Luerbio ^{[3
]}

de Figueiredo, Celina M. H. ^{[1
]}

Gutierrez, Marisa ^{[2
]}

机构：

[1] Univ Fed Rio de Janeiro, COPPE, Programa Engn Sistemas & Computacao, Rio de Janeiro, Brazil

[2] UNLP, Dept Matemat, CONICET, La Plata, Buenos Aires, Argentina

[3] Univ Estado Rio De Janeiro, FFP, Dept Matemat, Rio De Janeiro, Brazil

来源：

THEORETICAL COMPUTER SCIENCE | 2009年 / 410卷 / 21-23期

关键词：

Clique graphs; NP-complete problems; Helly property; Intersection graphs; DIAMETERS;

D O I：

10.1016/j.tcs.2009.01.018

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A complete set of a graph G is a subset of vertices inducing a complete subgraph. A clique is a maximal complete set. Denote bye(G) the clique family of G. The clique graph of G, denoted by C(G), is the intersection graph of C(G). Say that G is a clique graph if there exists a graph H such that G = K(H). The clique graph recognition problem asks whether a given graph is a clique graph. A sufficient condition was given by Hamelink in 1968, and a characterization was proposed by Roberts and Spencer in 1971. However, the time complexity of the problem of recognizing clique graphs is a long-standing open question. We prove that the clique graph recognition problem is NP-complete. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：2072 / 2083

页数：12

共 50 条

[21] Graph reconstruction in the congested clique
Montealegre, R.
Perez-Salazar, S.
Rapaport, I
Todinca, I
JOURNAL OF COMPUTER AND SYSTEM SCIENCES, 2020, 113 (113) : 1 - 17
[22] The Complexity of the Fixed Clique Property
Schröder, Bernd
Journal of Graph Algorithms and Applications, 2024, 28 (01) : 351 - 363
[23] Contractibility and the clique graph operator
Larrion, F.
Pizana, M. A.
Villarroel-Flores, R.
DISCRETE MATHEMATICS, 2008, 308 (16) : 3461 - 3469
[24] Clique complexes and graph powers
Michał Adamaszek
Israel Journal of Mathematics, 2013, 196 : 295 - 319
[25] Minimum Clique-clique Dominating Laplacian Energy of a Graph
Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal
Karnataka
576104, India
IAENG Int. J. Comput. Sci., 4 (1-5):
[26] Clique covering number a clind clique partition number on the line graph and total graph of n-Sun graph
Wuhan Gongye Daxue Xuebao, 2 (116-118):
[27] A POLYNOMIAL ALGORITHM FOR CONSTRUCTING THE CLIQUE GRAPH OF A LINE GRAPH
HEDMAN, B
DISCRETE APPLIED MATHEMATICS, 1986, 15 (01) : 61 - 66
[28] The Complexity of Helly-B1-EPG graph Recognition
Bornstein, Claudson F.
Golumbic, Martin Charles
Santos, Tanilson D.
Souza, Ueyerton S.
Szwarcfiter, Jayme L.
DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 2020, 22 (01):
[29] The complexity of cover graph recognition for some varieties of finite lattices
Rodl, V
Thoma, L
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 1995, 12 (04): : 351 - 374
[30] ON THE NUMBER OF DISTINCT MINIMAL CLIQUE PARTITIONS AND CLIQUE COVERS OF A LINE GRAPH
MCGUINNESS, S
REES, R
DISCRETE MATHEMATICS, 1990, 83 (01) : 49 - 62

← 1 2 3 4 5 →