Complexity results on graphs with few cliques

被引:0
作者
Rosgen, Bill [1 ]
Stewart, Lorna [2 ]
机构
[1] Univ Waterloo, Sch Comp Sci, Inst Quantum Computing, Waterloo, ON, Canada
[2] Univ Alberta, Dept Comp Sci, Edmonton, AB, Canada
关键词
graphs; few cliques; Helly property; intersection representation; complexity;
D O I
暂无
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
A graph class has few cliques if there is a polynomial bound on the number of maximal cliques contained in any member of the class. This restriction is equivalent to the requirement that any graph in the class has a polynomial sized intersection representation that satisfies the Helly property. On any such class of graphs some problems that are NP-complete on general graphs, such as the maximum clique problem and the maximum weighted clique problem, admit polynomial time algorithms. Other problems, such as the vertex clique cover and edge clique cover problems remain NP-complete on these classes. Several classes of graphs which have few cliques are discussed, and the complexity of some partitioning and covering problems are determined for the class of all graphs which have fewer cliques than a given polynomial bound.
引用
收藏
页码:127 / 135
页数:9
相关论文
共 19 条