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

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