Four NP-complete problems about generalizations of perfect graphs
Abstract
We show that the following problems are NP-complete. 1. Can the vertex set of a graph be partitioned into two sets such that each set induces a perfect graph? 2. Is the difference between the chromatic number and clique number at most for every induced subgraph of a graph? 3. Can the vertex set of every induced subgraph of a graph be partitioned into two sets such that the first set induces a perfect graph, and the clique number of the graph induced by the second set is smaller than that of the original induced subgraph? 4. Does a graph contain a stable set whose deletion results in a perfect graph? The proofs of the NP-completeness of the four problems follow the same pattern: Showing that all the four problems are NP-complete when restricted to triangle-free graphs by using results of Maffray and Preissmann on -colorability and -colorability of triangle-free graphs
Keywords
Cite
@article{arxiv.1705.05911,
title = {Four NP-complete problems about generalizations of perfect graphs},
author = {Vaidy Sivaraman},
journal= {arXiv preprint arXiv:1705.05911},
year = {2017}
}