Partitioning a graph into disjoint cliques and a triangle-free graph
نویسندگان
چکیده
منابع مشابه
Partitioning a graph into disjoint cliques and a triangle-free graph
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.
متن کاملThe 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 کاملNP-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 کاملPartitioning a graph into alliance free sets
A strong defensive alliance in a graph G = (V, E) is a set of vertices A ⊆ V , for which every vertex v ∈ A has at least as many neighbors in A as in V − A. We call a partition A, B of vertices to be an alliance-free partition, if neither A nor B contains a strong defensive alliance as a subset. We prove that a connected graph G has an alliance-free partition exactly when G has a block that is ...
متن کاملPartitioning a triangle-free planar graph into a forest and a forest of bounded degree
An (F , Fd)-partition of a graph is a vertex-partition into two sets F and Fd such that the graph induced by F is a forest and the one induced by Fd is a forest with maximum degree at most d. We prove that every triangle-free planar graph admits an (F , F5)-partition. Moreover we show that if for some integer d there exists a trianglefree planar graph that does not admit an (F , Fd)-partition, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2015
ISSN: 0166-218X
DOI: 10.1016/j.dam.2015.03.015