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- W2003128536 abstract "Polar and monopolar graphs are natural generalizations of bipartite and split graphs. A graph G=(V,E) is polar if its vertex set admits a partition V=A∪B such that A induces a complete multipartite graph and B the complement of a complete multipartite graph. If A is a stable set then G is called monopolar. This paper presents some sharp contrasts in the complexity of the recognition problem for monopolar graphs and for polar graphs. Among others we show that this problem is NP-complete for triangle-free planar graphs of maximum degree three, and is polynomially solvable on hole-free planar, chair-free planar and maximal planar graphs. We give a number of well-studied graph classes G together with a relatively small subclass H⊂G such that recognizing monopolar graphs in G is polynomial while recognizing polar graphs in H is NP-complete. Examples of such classes include the class of hole-free graphs G and its tiny subclass of {2K2,C5}-free co-planar graphs H, and the class of chair-free graphs G and its tiny subclass of 3K1-free co-planar graphs H. Our new NP-completeness results cover very restricted graph classes and sharpen known results, and the new positive results extend nearly all known results for monopolar recognition." @default.
- W2003128536 created "2016-06-24" @default.
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- W2003128536 date "2014-04-01" @default.
- W2003128536 modified "2023-09-27" @default.
- W2003128536 title "Complexity and algorithms for recognizing polar and monopolar graphs" @default.
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- W2003128536 doi "https://doi.org/10.1016/j.tcs.2014.01.032" @default.
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