Parameterized Algorithms for Recognizing Monopolar and 2-Subcolorable Graphs.
Journal of Computer and System Sciences(2018)
摘要
A graph G is a (ΠA,ΠB)-graph if V(G) can be bipartitioned into A and B such that G[A] satisfies property ΠA and G[B] satisfies property ΠB. The (ΠA,ΠB)-Recognition problem is to recognize whether a given graph is a (ΠA,ΠB)-graph. There are many (ΠA,ΠB)-Recognition problems, including the recognition problems for bipartite, split, and unipolar graphs. We present efficient algorithms for many cases of (ΠA,ΠB)-Recognition based on a technique which we dub inductive recognition. In particular, we give fixed-parameter algorithms for two NP-hard (ΠA,ΠB)-Recognition problems, Monopolar Recognition and 2-Subcoloring, parameterized by the number of maximal cliques in G[A]. We complement our algorithmic results with several hardness results for (ΠA,ΠB)-Recognition.
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关键词
Vertex-partition problems,Graph classes,Monopolar graphs,Subcolorings,Split graphs,Unipolar graphs,Fixed-parameter algorithms
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