Partitioning a graph into disjoint cliques and a triangle-free graph

نویسندگان

Faisal N. Abu-Khzam

Carl Feghali

Haiko Müller

چکیده

A (P3-free, K3-free)-colouring of a graph G = (V, E) is a partition of V = A ∪ B such that G[A] is P3-free and G[B] is K3-free. This problem is known to be NP-complete even when restricted to planar graphs and perfect graphs. In this paper, we provide a finite list of 17 forbidden induced subgraphs for cographs with a (P3-free, K3-free)colouring. This yields a linear time recognition algorithm.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

NP-hardness results for partitioning graphs into disjoint cliques and a triangle-free subgraph

This paper investigates the computational complexity of deciding whether the vertices of a graph can be partitioned into a disjoint union of cliques and a triangle-free subgraph. This problem is known to be NP-complete on arbitrary graphs. We show that this problem remains NP-complete even when restricted to planar graphs and perfect graphs.

متن کامل

The complexity of partitioning into disjoint cliques and a triangle-free graph

Motivated by Chudnovsky’s structure theorem of bull-free graphs, Abu-Khzam, Feghali, and Müller have recently proved that deciding if a graph has a vertex partition into disjoint cliques and a trianglefree graph is NP-complete for five graph classes. The problem is trivial for the intersection of these five classes. We prove that the problem is NP-complete for the intersection of two subsets of...

متن کامل

Cohen-Macaulay $r$-partite graphs with minimal clique cover

‎In this paper‎, ‎we give some necessary conditions for an $r$-partite graph such that the edge ring of the graph is Cohen-Macaulay‎. ‎It is proved that if there exists a cover of an $r$-partite Cohen-Macaulay graph by disjoint cliques of size $r$‎, ‎then such a cover is unique‎.

متن کامل

Approximation Algorithms for Clique Clustering

A clique clustering of a graph is a partitioning of its vertices into disjoint cliques. The quality of a clique clustering is measured by the total number of edges in its cliques. We consider the online variant of the clique clustering problem, where the vertices of the input graph arrive one at a time. At each step, the newly arrived vertex forms a singleton clique, and the algorithm can merge...

متن کامل