Parameterized Algorithms for Recognizing Monopolar and 2-Subcolorable Graphs

Iyad Kanj; Christian Komusiewicz; Manuel Sorge; Erik Jan van Leeuwen

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arXiv · 1702.04322

Parameterized Algorithms for Recognizing Monopolar and 2-Subcolorable Graphs

Iyad Kanj·Christian Komusiewicz·Manuel Sorge·Erik Jan van Leeuwen

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Abstract

A graph $G$ is a $(\Pi_A,\Pi_B)$-graph if $V(G)$ can be bipartitioned into $A$ and $B$ such that $G[A]$ satisfies property $\Pi_A$ and $G[B]$ satisfies property $\Pi_B$. The $(\Pi_{A},\Pi_{B})$-Recognition problem is to recognize whether a given graph is a $(\Pi_A,\Pi_B)$-graph. There are many $(\Pi_{A},\Pi_{B})$-Recognition problems, including the recognition problems for bipartite, split, and unipolar graphs. We present efficient algorithms for many cases of $(\Pi_A,\Pi_B)$-Recognition based on a technique which we dub inductive recognition. In particular, we give fixed-parameter algorithms for two NP-hard $(\Pi_{A},\Pi_{B})$-Recognition problems, Monopolar Recognition and 2-Subcoloring. We complement our algorithmic results with several hardness results for $(\Pi_{A},\Pi_{B})$-Recognition.

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Iyad Kanj, Christian Komusiewicz, Manuel Sorge, Erik Jan van Leeuwen. 2017-02-14. Parameterized Algorithms for Recognizing Monopolar and 2-Subcolorable Graphs. https://arxiv.org/abs/1702.04322

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