An efficiently solvable graph partition problem to which many problems are reducible
Information Processing Letters
Graph classes: a survey
Some optimal inapproximability results
Journal of the ACM (JACM)
Subgraph characterization of red/blue-split graph and kőnig egerváry graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Algorithms on Subtree Filament Graphs
Graph Theory, Computational Intelligence and Thought
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A multigraph G=(V,R@?B) with red and blue edges is an R/B-split graph if V is the union of a red and a blue stable set. Gavril has shown that R/B-split graphs yield a common generalization of split graphs and Konig-Egervary graphs. Moreover, R/B-split graphs can be recognized in linear time. In this note, we address the corresponding optimization problem: identify a set of vertices of maximal cardinality that decomposes into a red and a blue stable set. This problem is NP-hard in general. We investigate the complexity of special and related cases (e.g., (anti-)chains in partial orders and stable matroid bases) and exhibit some NP-hard cases as well as polynomial ones.