Partitions of graphs into one or two independent sets and cliques
Discrete Mathematics
Complexity of graph partition problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Graph classes: a survey
The complexity of some problems related to Graph 3-COLORABILITY
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Partitioning chordal graphs into independent sets and cliques
Discrete Applied Mathematics - Brazilian symposium on graphs, algorithms and combinatorics
Partition into cliques for cubic graphs: Planar case, complexity and approximation
Discrete Applied Mathematics
Finding odd cycle transversals
Operations Research Letters
Hi-index | 5.23 |
A cycle transversal (or feedback vertex set) of a graph G is a subset T@?V(G) such that T@?V(C)0@? for every cycle C of G. This work considers the problem of finding special cycle transversals in perfect graphs and cographs. We prove that finding a minimum cycle transversal T in a perfect graph G is NP-hard, even for bipartite graphs with maximum degree four. Since G-T is acyclic, this result implies that finding a maximum acyclic induced subgraph of a perfect graph is also NP-hard. Other special properties of T are considered. A clique (stable, respectively) cycle transversal, or simply cct (sct, respectively) is a cycle transversal which is a clique (stable set, respectively). Recognizing graphs which admit a cct can be done in polynomial time; however, no structural characterization of such graphs is known, even for perfect graphs. We characterize cographs with cct in terms of forbidden induced subgraphs and describe their structure. This leads to linear time recognition of cographs with cct. We also prove that deciding whether a perfect graph admits an sct is NP-complete. We characterize cographs with sct in terms of forbidden induced subgraphs; this characterization also leads to linear time recognition.